Pith. sign in

REVIEW 3 major objections 5 minor 62 references

The paper claims that a 3D convolutional autoencoder combined with a latent diffusion model can generate stable, statistically faithful electron-density trajectories from a compact latent space.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

A latent diffusion model conditioned on the current electron density state can generate future density fields for liquid lithium at 800 K with distributional and structural similarity to AIMD reference data.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection The paper applies latent diffusion to 3D electron density, but the global-average-pooling encoder makes the latent translation-invariant, so it cannot actually track the phase of the density, and the evidence is phase-blind. the 3 major comments →

arxiv 2509.00169 v1 pith:DOQ2A5IC submitted 2025-08-29 physics.comp-ph physics.chem-ph

Generative Latent Space Dynamics of Electron Density

Yuan Chiang , Youngsoo Choi , Daniel Osei-Kuffuor This is my paper
classification physics.comp-ph physics.chem-ph
keywords electron density dynamicslatent diffusion model3D convolutional autoencoderab initio molecular dynamicsliquid lithiumJensen-Shannon divergencegenerative time-series forecastinglog-normal density
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the time evolution of an electron density field, normally obtained from expensive ab initio molecular dynamics, can be learned and continued with a generative model operating on a compact latent representation. The pipeline encodes each three-dimensional density frame into a short latent vector with a 3D convolutional autoencoder, then trains a latent diffusion model to sample the next latent vector conditional on the current one, rolling the system forward autoregressively. On an 800 K liquid-lithium trajectory, the authors report stable long-horizon forecasts that reproduce both the spatial correlations and the log-normal-like statistics of the density, provided a scaled Jensen-Shannon divergence loss is added. If correct, this offers a route to cheap conditional sampling of electron densities for spectroscopy and related quantum dynamics, without the drift or collapse they observe in neural-operator and Fourier-space alternatives.

Core claim

The central claim is that probabilistic generation in latent space, rather than direct regression on grid values, is what makes electron-density trajectory forecasting stable. After encoding each electron density frame with a 3D convolutional autoencoder into a compact 1D latent vector, a latent diffusion model learns the conditional distribution of the next latent state given the current one. At inference, sampling from that conditional distribution produces the next density field, and repeating the step yields an autoregressive trajectory. The authors demonstrate on liquid lithium at 800 K that this produces visually and statistically consistent densities over an unseen test window, matchi

What carries the argument

The key mechanism is a two-stage generative model. A 3D convolutional autoencoder with circular padding and a global average pooling bottleneck compresses each normalized density frame into a fixed-size 1D latent vector; the average pooling enforces translation invariance, which the authors identify as the reason the latent dynamics do not drift. A diffusion model then acts in that latent space: noise is added to the latent of the next frame, and a small MLP denoiser conditioned on the current latent vector learns to remove it. A log-normal normalization with fixed parameters turns the raw density into an approximately standard-normal field, giving the decoder a convenient reconstruction spa

Load-bearing premise

The load-bearing premise is that electron density is approximately log-normal with the same fixed mean and variance everywhere, a property the paper checks on only one trajectory of one element, so any material or phase with a different density distribution would break the normalization the whole model relies on.

What would settle it

Take a held-out AIMD trajectory of a different material or phase, say silicon at high temperature or water, and compute ln rho over space and time; if its histogram is not approximately Gaussian with mean near -2.911 and variance near 0.271, then the normalization in eq. (6) misfits and the trained dynamics should visibly degrade in MSE and structure-factor comparisons on that system.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Long-horizon rollouts: the generated trajectory stays stable over the unrolled test window, while direct Fourier-space and neural-operator baselines drift or collapse, making the method a candidate surrogate for AIMD density evolution.
  • Statistical fidelity: generated densities match the reference probability distribution and structure factor S(q), so observables that depend on the density distribution, not just pointwise values, can be read off the generated fields.
  • Translation invariance: the average-pooling bottleneck renders the latent representation invariant to spatial shifts, which is why the model avoids the drift seen in phase-unstable Fourier representations; this suggests a concrete architectural rule for 3D field forecasting.
  • Conditional sampling: because each next state is sampled rather than regressed, the model does not collapse to a fuzzy average, a failure mode that occurs when most grid points have near-zero density; the sJSD term is what prevents this collapse.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The fixed log-normal normalization couples the whole approach to one empirical distribution. An untested but natural extension is to make the normalization parameters learnable or system-dependent, or to replace the transform with a learned bijection; if other materials deviate from log-normal density statistics, the model would need that change to transfer.
  • Because the authors only demonstrate a single-element NVT system, the stability claim is not yet established for changing cells or mixed species. Since they note the lattice constant could be concatenated back into the latent state, a concrete next test is a constant-pressure or two-element trajectory.
  • The structure-factor comparison shows the sJSD model trades some short-wavelength fidelity for long-wavelength distributional matching. A multi-scale or spectral-weighted loss is a plausible, untested modification that could retain both, and would give a sharper test of whether distribution matching is the right regularizer.
  • The physical timestep is fixed at the 2 fs AIMD interval. A testable extension is to let the conditional diffusion model jump multiple timesteps at once; if multi-step latent sampling works, the method becomes a genuinely accelerated dynamics surrogate rather than a trajectory interpolator.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes a generative framework for forecasting electron density trajectories from AIMD simulations. A 3D convolutional autoencoder compresses each density frame into a 1D latent vector, and a latent diffusion model is trained to generate the next latent state conditioned on the current one. A scaled Jensen–Shannon divergence (sJSD) loss is added to preserve the statistical distribution of the generated densities. The method is demonstrated on a single 10 ps AIMD trajectory of liquid lithium at 800 K (32 atoms), with the first 8 ps used for training and the last 2 ps as test. The authors claim stable long-horizon rollouts and accurate capture of both spatial correlations (via S(q)) and the log-normal-like density distribution. The paper also discusses limitations, including the lack of equivariance to translations and the need for multi-species generalization.

Significance. If the central claim were fully supported, this would be a useful contribution to the emerging area of ML surrogates for quantum-mechanical dynamics. Combining latent diffusion with a volumetric autoencoder and a distribution-matching regularizer is a plausible and timely idea, and the choice of electron density as the target variable is scientifically motivated. The authors honestly acknowledge several limitations, including the lack of translation-equivariant modeling and the restricted scope of the experiments. However, the evidence provided is mostly qualitative and does not establish the strongest claims made in the abstract and Section 3. The paper is not internally inconsistent, but the gap between the stated claims and the evaluation is substantial.

major comments (3)
  1. [§2.2, eq. (8), Fig. 3–4] The encoder ends with global average pooling after strided convolutions with circular padding, which makes the latent representation invariant to global translations of the input density. The state in eq. (8) excludes ionic positions and lattice parameters, and no positional/equivariant channel is described. Consequently, the latent z(τ) cannot encode the phase (absolute position) of density peaks, and the conditional denoiser pθ(z(τ+Δτ)|z(τ)) cannot track a translated density. The abstract's claim that the model 'predicts their future states' is therefore not supported by the architecture. The validation in Fig. 4 uses histograms and spherically averaged S(q), both of which are insensitive to translations, and Fig. 3 shows only a single visual trajectory. The authors themselves note in §5 that 'future investigation of models that are equivariant to phase shift and robust to translation
  2. [§3, Figs. 3–4] The central quantitative claims—'stable long-horizon rollouts without drift or collapse' and accurate spatial/statistical fidelity—are supported only by a single 140-step rollout (Fig. 3) and distributional comparisons (Fig. 4). There are no numerical error metrics (e.g., per-frame RMSE, MAE, correlation, drift rate, or collapse frequency), no error bars, no repeated rollouts from different seeds, and no baselines (e.g., persistence, mean-field prediction, or a standard LDM without sJSD on the same architecture). The test set is a 2 ps continuation of the same 10 ps AIMD trajectory, so the generalization claim is limited to a short extrapolation of one system. This does not meet the standard of evidence for 'long-horizon' stability or for the claimed superiority over other approaches mentioned in §5. Please add quantitative metrics and baselines.
  3. [§2.1, Proposition 1, eq. (6), Fig. 4] The log-normal hypothesis is labeled 'Proposition 1' but is an empirical observation supported only by a visual histogram of one training trajectory (Fig. 1, bottom). The normalization in eq. (6) uses fixed μ and σ from the training set, and the sJSD loss (§2.2, eq. (14)) directly optimizes the histogram match between generated and target densities. Therefore the agreement shown in Fig. 4 is partly a consequence of the training objective, not an independent confirmation that the model 'captures' the log-normal structure. The paper should present a quantitative goodness-of-fit test for the log-normal assumption, validate it on a held-out trajectory or another material, and clearly separate the role of the sJSD loss from an emergent property of the learned dynamics.
minor comments (5)
  1. [§2.2] Equation (10) writes p(z_T) = N(x_T; 0, I) with x_T undefined; should be z_T. Also, in eq. (12), the conditioning notation z_t(τ + Δτ) is not defined precisely; clarify that z_t is the noised latent at diffusion step t for the target frame.
  2. [§3] The hyperparameters λ1=0.1 and λ2=10 are given, but no sensitivity analysis or ablation is provided. The latent dimension c, number of diffusion steps T, noise schedule, network sizes, and training details are omitted, making the experiments difficult to reproduce.
  3. [§2.1] Calling the log-normal observation a 'Proposition' is misleading; it is an empirical assumption. Also, the statement 'roughly log-normally distributed' should be supported by a quantitative test (e.g., Q-Q plot or Kolmogorov–Smirnov statistic).
  4. [Appendix A] The quantity S(q) is defined as the spherical average of |F(q)| (amplitude spectrum), whereas the conventional static structure factor usually refers to intensity |F(q)|^2. Please clarify this choice and its implications for comparing with literature values.
  5. [Throughout] There are several typos and formatting issues: 'traejctories' in Fig. 3, 'the the', 'kernal PCA', and inconsistent reference formatting (e.g., ref. [56]). Also, the paper does not mention data/code availability; for a computational study, sharing code and trained models would strengthen reproducibility.

Circularity Check

1 steps flagged

Partial circularity: the claimed capture of the log-normal density distribution is the sJSD training objective itself; the core latent-dynamics and S(q) checks are independent.

specific steps
  1. fitted input called prediction [Sec. 2.2 (Loss and regularization, Eqs. 13–15); Sec. 3 (Fig. 4); Abstract]
    "To ensure that the statistical distribution of the generated electron density matches the ground truth, we incorporate a smooth, differentiable version of the Jensen-Shannon Divergence (JSD) as a loss term. ... The model trained with sJSD loss clearly demonstrates more similar distribution to test trajectory than the one without sJSD regularization."

    The training objective in Eq. (15) directly includes λ2 LsJSD, which minimizes the Jensen-Shannon divergence between the reconstructed density distribution P and the ground-truth distribution Q (Eq. 14). Therefore, the abstract's claim that the model 'accurately captures ... the log-normal-like statistical structure of the density' is essentially a restatement of what the loss was constructed to enforce, not an independent discovery. The log-normal shape is also partly baked in through the logarithmic normalization in Eq. (6) with fixed µ = −2.911, σ = 0.271. The S(q) comparison is a separate, non-optimized spatial-structure check and provides independent support, which keeps the circularity partial rather than total.

full rationale

The core generative-dynamics pipeline—3D convolutional autoencoder plus latent diffusion with autoregressive conditioning (Eqs. 9–12)—is self-contained and evaluated against a held-out AIMD trajectory; the long-horizon rollout/stability claim does not reduce to the training inputs. The notable circularity is limited to the distributional-fidelity claim: the sJSD loss (Eq. 14) is explicitly designed to match generated and reference histograms, so reporting that the sJSD model yields a similar distribution (Fig. 4) is the optimization objective presented as a result. The spatial-correlation check via S(q) is genuinely independent and supports the method. Self-citations ([24]–[42], [62]) appear in related-work and dimensionality-reduction contexts; they are not load-bearing for the derivation and no uniqueness theorem is imported. The paper itself flags the translation-invariance/phase limitation in Sec. 5 ('The future investigation of models that are equivariant to phase shift and robust to translation will be important'), and Proposition 1 is verified only on a single Li trajectory with the training set visualized; these are correctness/generality concerns, not circularity. Overall the central derivation is independent, with one partially circular distributional claim, giving score 4.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The central claims rest on the log-normal distribution hypothesis, the pseudo-density modeling choice, the Markovian state assumption, and the standard LDM smoothness assumption. Free parameters include the log-normal normalization statistics and the loss weights, all fitted to the training data.

free parameters (5)
  • Log-normal normalization mean mu = -2.911
    Fitted to the training set and used in eq. (6) to normalize all density data.
  • Log-normal normalization std sigma = 0.271
    Fitted to the training set and used in eq. (6) to normalize all density data.
  • Loss weight lambda1 = 0.1
    Weight on the diffusion denoising loss in eq. (15), chosen empirically.
  • Loss weight lambda2 = 10
    Weight on the sJSD loss in eq. (15), chosen empirically after 'empirical test'.
  • Latent dimension c
    Bottleneck size of the autoencoder; not reported in the paper, affects reconstruction fidelity and dynamics.
axioms (4)
  • domain assumption Electron density is approximately log-normally distributed over space and time in equilibrated AIMD trajectories (Proposition 1).
    Stated as Proposition 1 without proof; only demonstrated on the Li32 system. Used to define the log normalization in eq. (6).
  • domain assumption The pseudo (PAW) electron density is a sufficient learning target.
    Section 2.1: the authors discard the total density and train only on the variationally optimized pseudo density.
  • domain assumption The state (rho, rhodot) at time tau is a sufficient statistic for predicting rho at tau+Delta tau.
    The conditional diffusion model in eq. (12) uses only z0(tau) to generate z0(tau+Delta tau), ignoring longer histories and explicit ionic coordinates.
  • standard math The learned latent space is a smooth low-dimensional manifold on which diffusion and denoising can operate.
    Standard LDM assumption; the authors provide no convergence or smoothness analysis.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Generative Latent Space Dynamics of Electron Density." pith.science (2026). https://pith.science/paper/DOQ2A5IC

@misc{pith2026250900169,
  author       = {Pith},
  title        = {Pith review of: Generative Latent Space Dynamics of Electron Density},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DOQ2A5IC}},
  note         = {Machine review of arXiv:2509.00169}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while machine learning methods have advanced static density prediction, modeling its spatiotemporal dynamics remains largely unexplored. In this work, we introduce a generative framework that combines a 3D convolutional autoencoder with a latent diffusion model (LDM) to learn electron density trajectories from ab-initio molecular dynamics (AIMD) simulations. Our method encodes electron densities into a compact latent space and predicts their future states by sampling from the learned conditional distribution, enabling stable long-horizon rollouts without drift or collapse. To preserve statistical fidelity, we incorporate a scaled Jensen-Shannon divergence regularization that aligns generated and reference density distributions. On AIMD trajectories of liquid lithium at 800 K, our model accurately captures both the spatial correlations and the log-normal-like statistical structure of the density. The proposed framework has the potential to accelerate the simulation of quantum dynamics and overcome key challenges faced by current spatiotemporal machine learning methods as surrogates of quantum mechanical simulators.

Figures

Figures reproduced from arXiv: 2509.00169 by Daniel Osei-Kuffuor, Youngsoo Choi, Yuan Chiang.

Figure 1
Figure 1. Figure 1: Data distribution. Pseudo electron density dis￾tribution of Li32 trajectory approximately follows single log-normal distribution with µ = −2.911, σ = 0.271. Only training set is visualized. State representation. The state space of the classical atomistic system is determined by atomic positions and velocities. Similarly, in order to be complete, the state of the electron density should be at least describe… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of latent space generative process to emulate the dynamics of electron density through the combination of autoencoder and latent diffusion model. At each physical time step τ , the model conditions the latent denoiser with the current latent state z0(τ ) to predict the next latent state z0(τ + ∆τ ). The decoder maps the latent state back to physical space s˜(τ + ∆τ ) = D(z0(τ + ∆τ )). modifica… view at source ↗
Figure 3
Figure 3. Figure 3: Autoregressive trajectories. LDM generates and evolves electron density qualitatively consistent with unseen test trajectory of Li atoms at 800 K. The model trained with sJSD loss has less delocalized electron distribution similar to the ground truth. 2D slices at the middle plane along x direction are shown. The grid values presented are normalized pseudo charge density ρ˜ (eq. (6), fig. 1). See [PITH_FU… view at source ↗
Figure 4
Figure 4. Figure 4: Statistical consistency of generated trajectories. Probability distribution and static structure factor S(q) of test-set (ground-truth) and generated (forecast) electron densities. The LDM model trained with sJSD loss outperforms the model without sJSD. The static structure factor is obtained by averaging over the unrolled trajectory frames. The detailed S(q) calculation can be found in Appendix A. evolves… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

62 extracted references · 43 canonical work pages

  1. [1]

    Accuracy of charge densities in electronic structure calculations

    Moritz Gubler, Moritz R Schäfer, Jörg Behler, and Stefan Goedecker. Accuracy of charge densities in electronic structure calculations. The Journal of Chemical Physics, 162(9), 2025

    work page 2025

  2. [2]

    Convergence acceleration of iterative sequences

    Péter Pulay. Convergence acceleration of iterative sequences. the case of scf iteration. Chemical physics letters, 73(2):393–398, 1980

    work page 1980

  3. [3]

    A class of methods for solving nonlinear simultaneous equations

    Charles G Broyden. A class of methods for solving nonlinear simultaneous equations. Mathe- matics of computation, 19(92):577–593, 1965

    work page 1965

  4. [4]

    Accelerating self-consistent field iterations in kohn-sham density functional theory using a low-rank approximation of the dielectric matrix

    Sambit Das and Vikram Gavini. Accelerating self-consistent field iterations in kohn-sham density functional theory using a low-rank approximation of the dielectric matrix. Physical Review B, 107(12):125133, 2023

    work page 2023

  5. [5]

    A recipe for charge density prediction

    Xiang Fu, Andrew Rosen, Kyle Bystrom, Rui Wang, Albert Musaelian, Boris Kozinsky, Tess Smidt, and Tommi Jaakkola. A recipe for charge density prediction. Advances in Neural Information Processing Systems, 37:9727–9752, 2024

    work page 2024

  6. [6]

    Higher-order equivariant neural networks for charge density prediction in materials

    Teddy Koker, Keegan Quigley, Eric Taw, Kevin Tibbetts, and Lin Li. Higher-order equivariant neural networks for charge density prediction in materials. npj Computational Materials, 10(1): 161, 2024

    work page 2024

  7. [7]

    Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids

    Peter Bjørn Jørgensen and Arghya Bhowmik. Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids. npj Computational Materials, 8(1):183, 2022

    work page 2022

  8. [8]

    Deepdft: Neural message passing network for accurate charge density prediction

    Peter Bjørn Jørgensen and Arghya Bhowmik. Deepdft: Neural message passing network for accurate charge density prediction. arXiv preprint arXiv:2011.03346, 2020. 8

    Pith/arXiv arXiv 2011

  9. [9]

    Machine learning electron density prediction using weighted smooth overlap of atomic positions

    Siddarth K Achar, Leonardo Bernasconi, and J Karl Johnson. Machine learning electron density prediction using weighted smooth overlap of atomic positions. Nanomaterials, 13(12):1853, 2023

    work page 2023

  10. [10]

    Image super-resolution inspired electron density prediction

    Chenghan Li, Or Sharir, Shunyue Yuan, and Garnet Kin-Lic Chan. Image super-resolution inspired electron density prediction. Nature Communications, 16(1):4811, 2025

    work page 2025

  11. [11]

    High- resolution image synthesis with latent diffusion models

    Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High- resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684–10695, 2022

    2022

  12. [12]

    Gpaw: An open python package for electronic structure calculations

    Jens Jørgen Mortensen, Ask Hjorth Larsen, Mikael Kuisma, Aleksei V Ivanov, Alireza Taghizadeh, Andrew Peterson, Anubhab Haldar, Asmus Ougaard Dohn, Christian Schäfer, Elvar Örn Jónsson, et al. Gpaw: An open python package for electronic structure calculations. The Journal of Chemical Physics, 160(9), 2024

    work page 2024

  13. [13]

    The atomic simulation environment—a python library for working with atoms

    Ask Hjorth Larsen, Jens Jørgen Mortensen, Jakob Blomqvist, Ivano E Castelli, Rune Christensen, Marcin Dułak, Jesper Friis, Michael N Groves, Bjørk Hammer, Cory Hargus, et al. The atomic simulation environment—a python library for working with atoms. Journal of Physics: Condensed Matter, 29(27):273002, 2017

    work page 2017

  14. [14]

    Projector augmented-wave method

    Peter E Blöchl. Projector augmented-wave method. Physical review B, 50(24):17953, 1994

    work page 1994

  15. [15]

    Real-space grid implementation of the projector augmented wave method

    Jens Jørgen Mortensen, Lars Bruno Hansen, and Karsten Wedel Jacobsen. Real-space grid implementation of the projector augmented wave method. Physical Review B—Condensed Matter and Materials Physics, 71(3):035109, 2005

    work page 2005

  16. [16]

    Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position

    Kunihiko Fukushima. Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biological cybernetics, 36(4):193–202, 1980

    work page 1980

  17. [17]

    Gradient-based learning applied to document recognition

    Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 2002

    work page 2002

  18. [18]

    Imagenet classification with deep convolutional neural networks

    Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25, 2012

    2012

  19. [19]

    Deep residual learning for image recognition, 2015

    Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition, 2015. URL https://arxiv.org/abs/1512.03385

    Pith/arXiv arXiv 2015

  20. [20]

    Fast and accurate deep network learning by exponential linear units (elus)

    Djork-Arné Clevert, Thomas Unterthiner, and Sepp Hochreiter. Fast and accurate deep network learning by exponential linear units (elus). arXiv preprint arXiv:1511.07289, 4(5):11, 2015

    Pith/arXiv arXiv 2015

  21. [21]

    Denoising diffusion probabilistic models

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840–6851, 2020

    2020

  22. [22]

    Generative modeling by estimating gradients of the data distribution

    Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019

    2019

  23. [23]

    Generalized jensen-shannon divergence loss for learning with noisy labels

    Erik Englesson and Hossein Azizpour. Generalized jensen-shannon divergence loss for learning with noisy labels. Advances in Neural Information Processing Systems, 34:30284–30297, 2021

    work page 2021

  24. [24]

    Efficient space–time reduced order model for linear dynamical systems in python using less than 120 lines of code

    Youngkyu Kim, Karen Wang, and Youngsoo Choi. Efficient space–time reduced order model for linear dynamical systems in python using less than 120 lines of code. Mathematics, 9(14): 1690, 2021

    work page 2021

  25. [25]

    Component-wise reduced order model lattice-type structure design

    Sean McBane and Youngsoo Choi. Component-wise reduced order model lattice-type structure design. Computer methods in applied mechanics and engineering, 381:113813, 2021

    work page 2021

  26. [26]

    Gradient-based constrained optimization using a database of linear reduced-order models

    Youngsoo Choi, Gabriele Boncoraglio, Spenser Anderson, David Amsallem, and Charbel Farhat. Gradient-based constrained optimization using a database of linear reduced-order models. Journal of Computational Physics, 423:109787, 2020

    work page 2020

  27. [27]

    Space–time least-squares petrov–galerkin projection for nonlinear model reduction

    Youngsoo Choi and Kevin Carlberg. Space–time least-squares petrov–galerkin projection for nonlinear model reduction. SIAM Journal on Scientific Computing, 41(1):A26–A58, 2019. 9

    work page 2019

  28. [28]

    Reduced order models for lagrangian hydrodynamics

    Dylan Matthew Copeland, Siu Wun Cheung, Kevin Huynh, and Youngsoo Choi. Reduced order models for lagrangian hydrodynamics. Computer Methods in Applied Mechanics and Engineering, 388:114259, 2022

    work page 2022

  29. [29]

    Space–time reduced order model for large-scale linear dynamical systems with application to boltzmann transport problems

    Youngsoo Choi, Peter Brown, William Arrighi, Robert Anderson, and Kevin Huynh. Space–time reduced order model for large-scale linear dynamical systems with application to boltzmann transport problems. Journal of Computational Physics, 424:109845, 2021

    work page 2021

  30. [30]

    Sns: A solution-based nonlinear subspace method for time-dependent model order reduction

    Youngsoo Choi, Deshawn Coombs, and Robert Anderson. Sns: A solution-based nonlinear subspace method for time-dependent model order reduction. SIAM Journal on Scientific Computing, 42(2):A1116–A1146, 2020

    work page 2020

  31. [31]

    S-opt: A points selection algorithm for hyper-reduction in reduced order models

    Jessica T Lauzon, Siu Wun Cheung, Yeonjong Shin, Youngsoo Choi, Dylan M Copeland, and Kevin Huynh. S-opt: A points selection algorithm for hyper-reduction in reduced order models. SIAM Journal on Scientific Computing, 46(4):B474–B501, 2024

    work page 2024

  32. [32]

    Local la- grangian reduced-order modeling for the rayleigh-taylor instability by solution manifold decom- position

    Siu Wun Cheung, Youngsoo Choi, Dylan Matthew Copeland, and Kevin Huynh. Local la- grangian reduced-order modeling for the rayleigh-taylor instability by solution manifold decom- position. Journal of Computational Physics, 472:111655, 2023

    work page 2023

  33. [33]

    Multidimensional scaling

    Mark L Davison and Stephen G Sireci. Multidimensional scaling. In Handbook of applied multivariate statistics and mathematical modeling, pages 323–352. Elsevier, 2000

    work page 2000

  34. [34]

    A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

    Youngkyu Kim, Youngsoo Choi, David Widemann, and Tarek Zohdi. A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder. Journal of Computational Physics, 451:110841, 2022

    work page 2022

  35. [35]

    A fast and accurate do- main decomposition nonlinear manifold reduced order model

    Alejandro N Diaz, Youngsoo Choi, and Matthias Heinkenschloss. A fast and accurate do- main decomposition nonlinear manifold reduced order model. Computer Methods in Applied Mechanics and Engineering, 425:116943, 2024

    work page 2024

  36. [36]

    Lasdi: Parametric latent space dynamics identification

    William D Fries, Xiaolong He, and Youngsoo Choi. Lasdi: Parametric latent space dynamics identification. Computer Methods in Applied Mechanics and Engineering, 399:115436, 2022

    work page 2022

  37. [37]

    glasdi: Parametric physics-informed greedy latent space dynamics identification

    Xiaolong He, Youngsoo Choi, William D Fries, Jonathan L Belof, and Jiun-Shyan Chen. glasdi: Parametric physics-informed greedy latent space dynamics identification. Journal of Computational Physics, 489:112267, 2023

    work page 2023

  38. [38]

    Gplasdi: Gaus- sian process-based interpretable latent space dynamics identification through deep autoencoder

    Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, and Jonathan L Belof. Gplasdi: Gaus- sian process-based interpretable latent space dynamics identification through deep autoencoder. Computer Methods in Applied Mechanics and Engineering, 418:116535, 2024

    work page 2024

  39. [39]

    Weak-form latent space dynamics identification

    April Tran, Xiaolong He, Daniel A Messenger, Youngsoo Choi, and David M Bortz. Weak-form latent space dynamics identification. Computer Methods in Applied Mechanics and Engineering, 427:116998, 2024

    work page 2024

  40. [40]

    tlasdi: Thermodynamics-informed latent space dynamics identification

    Jun Sur Richard Park, Siu Wun Cheung, Youngsoo Choi, and Yeonjong Shin. tlasdi: Thermodynamics-informed latent space dynamics identification. Computer Methods in Applied Mechanics and Engineering, 429:117144, 2024

    work page 2024

  41. [41]

    Physics-informed active learning with simultaneous weak-form latent space dynamics identification

    Xiaolong He, April Tran, David M Bortz, and Youngsoo Choi. Physics-informed active learning with simultaneous weak-form latent space dynamics identification. International Journal for Numerical Methods in Engineering, 126(1):e7634, 2025

    work page 2025

  42. [42]

    Teeratorn Kadeethum, Francesco Ballarin, Youngsoo Choi, Daniel O’Malley, Hongkyu Yoon, and Nikolaos Bouklas. Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques.Advances in Water Resources, 160:104098, 2022

    work page 2022

  43. [43]

    A global geometric framework for nonlinear dimensionality reduction

    Joshua B Tenenbaum, Vin de Silva, and John C Langford. A global geometric framework for nonlinear dimensionality reduction. science, 290(5500):2319–2323, 2000

    2000

  44. [44]

    Manifold learning: What, how, and why

    Marina Meil˘a and Hanyu Zhang. Manifold learning: What, how, and why. Annual Review of Statistics and Its Application, 11(1):393–417, 2024. 10

    work page 2024

  45. [45]

    Fourier neural operator for parametric partial differen- tial equations

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differen- tial equations. arXiv preprint arXiv:2010.08895, 2020

    Pith/arXiv arXiv 2010

  46. [46]

    Factorized fourier neural operators

    Alasdair Tran, Alexander Mathews, Lexing Xie, and Cheng Soon Ong. Factorized fourier neural operators. arXiv preprint arXiv:2111.13802, 2021

    Pith/arXiv arXiv 2021

  47. [47]

    Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

    Lu Lu, Pengzhan Jin, and George Em Karniadakis. Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193, 2019

    Pith/arXiv arXiv 1910

  48. [48]

    Disco: learning to discover an evolution operator for multi-physics-agnostic prediction

    Rudy Morel, Jiequn Han, and Edouard Oyallon. Disco: learning to discover an evolution operator for multi-physics-agnostic prediction. arXiv preprint arXiv:2504.19496, 2025

    Pith/arXiv arXiv 2025

  49. [49]

    Hamiltonian systems and transformation in hilbert space

    Bernard O Koopman. Hamiltonian systems and transformation in hilbert space. Proceedings of the National Academy of Sciences, 17(5):315–318, 1931

    work page 1931

  50. [50]

    Score dynamics: Scaling molecular dynamics with picoseconds time steps via conditional diffusion model

    Tim Hsu, Babak Sadigh, Vasily Bulatov, and Fei Zhou. Score dynamics: Scaling molecular dynamics with picoseconds time steps via conditional diffusion model. Journal of Chemical Theory and Computation, 20(6):2335–2348, 2024

    work page 2024

  51. [51]

    Lost in latent space: An empirical study of latent diffusion models for physics emulation

    François Rozet, Ruben Ohana, Michael McCabe, Gilles Louppe, François Lanusse, and Shirley Ho. Lost in latent space: An empirical study of latent diffusion models for physics emulation. arXiv preprint arXiv:2507.02608, 2025

    arXiv 2025

  52. [52]

    Neural ordinary differential equations

    Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud. Neural ordinary differential equations. Advances in neural information processing systems, 31, 2018

    2018

  53. [53]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

    Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378:686–707, 2019

    2019

  54. [54]

    Scientific machine learning through physics–informed neural networks: Where we are and what’s next

    Salvatore Cuomo, Vincenzo Schiano Di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, and Francesco Piccialli. Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Journal of Scientific Computing, 92(3):88, 2022

    2022

  55. [55]

    Fourcastnet: Accel- erating global high-resolution weather forecasting using adaptive fourier neural operators

    Thorsten Kurth, Shashank Subramanian, Peter Harrington, Jaideep Pathak, Morteza Mardani, David Hall, Andrea Miele, Karthik Kashinath, and Anima Anandkumar. Fourcastnet: Accel- erating global high-resolution weather forecasting using adaptive fourier neural operators. In Proceedings of the platform for advanced scientific computing conference, pages 1–11, 2023

    2023

  56. [56]

    Elena, Dávid P

    Ilyes Batatia, Philipp Benner, Yuan Chiang, Alin M. Elena, Dávid P. Kovács, Janosh Riebesell, Xavier R. Advincula, Mark Asta, William J. Baldwin, Noam Bernstein, Arghya Bhowmik, Samuel M. Blau, Vlad C ˘arare, James P. Darby, Sandip De, Flaviano Della Pia, V olker L. Deringer, Rokas Elijošius, Zakariya El-Machachi, Edvin Fako, Andrea C. Ferrari, Annalena G...

    Pith/arXiv arXiv 2023

  57. [57]

    Density-functional theory for time-dependent systems

    Erich Runge and Eberhard KU Gross. Density-functional theory for time-dependent systems. Physical review letters, 52(12):997, 1984

    work page 1984

  58. [58]

    The equation of motion coupled-cluster method

    John F Stanton and Rodney J Bartlett. The equation of motion coupled-cluster method. a systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties. The Journal of chemical physics, 98(9):7029–7039, 1993. 11

    work page 1993

  59. [59]

    Orbital-free density functional theory: An attractive electronic structure method for large-scale first-principles simulations

    Wenhui Mi, Kai Luo, SB Trickey, and Michele Pavanello. Orbital-free density functional theory: An attractive electronic structure method for large-scale first-principles simulations. Chemical Reviews, 123(21):12039–12104, 2023

    work page 2023

  60. [60]

    An introduction to orbital-free density functional theory

    Vincent L Lignères and Emily A Carter. An introduction to orbital-free density functional theory. In Handbook of materials modeling: methods, pages 137–148. Springer, 2005

    work page 2005

  61. [61]

    Time-dependent orbital-free density functional theory: Background and pauli kernel approximations

    Kaili Jiang and Michele Pavanello. Time-dependent orbital-free density functional theory: Background and pauli kernel approximations. Physical Review B, 103(24):245102, 2021

    work page 2021

  62. [62]

    Defining foundation models for computational science: A call for clarity and rigor

    Youngsoo Choi, Siu Wun Cheung, Youngkyu Kim, Ping-Hsuan Tsai, Alejandro N Diaz, Ivan Zanardi, Seung Whan Chung, Dylan Matthew Copeland, Coleman Kendrick, William Anderson, et al. Defining foundation models for computational science: A call for clarity and rigor. arXiv preprint arXiv:2505.22904, 2025. 12 A Structure factor S(q) calculation We compute the c...

    Pith/arXiv arXiv 2025

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.