Extends structural identifiability analysis to functional components of differential equation models and characterizes conditions for unique recovery using differential algebra techniques.
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Physics-informed machine learning
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HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
Structural identifiability analysis shows point sources restore identifiability for inferring spatial stochastic dynamics parameters from static snapshots, unlike distributed sources, with limits depending on modeling choices.
Optimizing training data via a differentiable SCM yields climate emulators that outperform those trained on six standard ScenarioMIP pathways while using less data and isolating distinct forcing responses.
LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
A domain-validity rubric and MR-card format screen candidate metamorphic relations into auditable test assets for SciML surrogates, separating model violations from out-of-domain applications.
MeshTok uses AMR-inspired adaptive multiscale tokenization to improve the efficiency-accuracy trade-off of Transformer models for PDEs over uniform-grid baselines.
TokaMind, pre-trained on MAST tokamak data, transfers to power grid PMU data for severe event classification with F1 0.837, where difficulty depends on grid topology and CSD indicators boost early-warning performance over CNN baselines.
A per-layer risk estimator for hybrid deep networks shows that replacing learned layers with known operators shrinks the bound and scales sample needs with the number of replaced parameters, validated on CT reconstruction.
A video-to-PDE pipeline extracts the model u_t + v(t)·∇u = 9.005|∇u|^2 + 0.666Δu from grayscale ink-plume footage, outperforming advection-diffusion baselines on held-out frames and reducing to linear form via Cole-Hopf transformation.
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
JAX-FVM is a differentiable, entropy-stable finite volume solver for 2D compressible Euler/Navier-Stokes equations on unstructured meshes, built in JAX.
A per-instance learned graph-network transfer between coarse and fine discrete-field optimizations improves Darcy and EIT coefficient reconstructions without surrogates or pretraining.
A physics-informed self-supervised framework learns detector calibration parameters and ionic charge-state predictions jointly from raw spectrometer data using iterative pseudo-labelling driven by physical constraints.
A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
Unified framework proves the score function yields the minimum-variance unbiased shear estimator and that response-weighted inverse-variance weights minimize shape noise independent of galaxy shape distributions, with RDSM reducing noise by ~17.5% at LSST depth.
A Fourier neural operator trained on Boussinesq-compressible simulation pairs corrects Boussinesq predictions for natural convection, achieving SSIM near unity and MSE reductions of one to three orders of magnitude.
SIES learns generalizable local coupling operators via signed source-target attention for controllable synchronization in graph dynamical systems and applies the principle to heterophilous graph representation learning.
A hybrid pre-trained and experimentally fine-tuned diffusion model denoises speckle data, cutting RMSE by up to 72% in femtometre-scale wavelength sensing with an integrating sphere where standard methods fail.
Hybrid neural-process model derives biokinetic parameters from genomic traits for soil organic matter turnover, with ecological constraints, and outperforms baselines on synthetic and real data.
QCPIKAN is a quantum-classical physics-informed KAN that claims exponential high-frequency error convergence and superior accuracy over prior QCPINNs on single-phase, transport, and two-phase seepage PDEs.
A PINN approach learns galactic gravitational potentials from acceleration data, achieving sub-percent errors on simulations while outperforming analytic models and retaining interpretability via structured priors.
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
An LLM-based self-evolving agent discovers a traveling-wave controller with body-frame guidance and yaw feedback that generalizes to unseen targets for an underactuated fluid swimmer.
citing papers explorer
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Structural functional identifiability and model discovery in differential equation models
Extends structural identifiability analysis to functional components of differential equation models and characterizes conditions for unique recovery using differential algebra techniques.
-
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
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Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots
Structural identifiability analysis shows point sources restore identifiability for inferring spatial stochastic dynamics parameters from static snapshots, unlike distributed sources, with limits depending on modeling choices.
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Optimal scenario design for climate emulation
Optimizing training data via a differentiable SCM yields climate emulators that outperform those trained on six standard ScenarioMIP pathways while using less data and isolating distinct forcing responses.
-
A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks
LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
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Domain-Validity-Gated Metamorphic Testing of Scientific ML Surrogates
A domain-validity rubric and MR-card format screen candidate metamorphic relations into auditable test assets for SciML surrogates, separating model violations from out-of-domain applications.
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MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers
MeshTok uses AMR-inspired adaptive multiscale tokenization to improve the efficiency-accuracy trade-off of Transformer models for PDEs over uniform-grid baselines.
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TokaMind for Power Grid: Cross-Domain Transfer from Fusion Plasma
TokaMind, pre-trained on MAST tokamak data, transfers to power grid PMU data for severe event classification with F1 0.837, where difficulty depends on grid topology and CSD indicators boost early-warning performance over CNN baselines.
-
A Deep Risk Estimator for Known Operator Learning
A per-layer risk estimator for hybrid deep networks shows that replacing learned layers with known operators shrinks the bound and scales sample needs with the number of replaced parameters, validated on CT reconstruction.
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From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamics
A video-to-PDE pipeline extracts the model u_t + v(t)·∇u = 9.005|∇u|^2 + 0.666Δu from grayscale ink-plume footage, outperforming advection-diffusion baselines on held-out frames and reducing to linear form via Cole-Hopf transformation.
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Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
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JAX-FVM: A differentiable, entropy-stable finite volume solver on unstructured meshes for compressible flows
JAX-FVM is a differentiable, entropy-stable finite volume solver for 2D compressible Euler/Navier-Stokes equations on unstructured meshes, built in JAX.
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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems
A per-instance learned graph-network transfer between coarse and fine discrete-field optimizations improves Darcy and EIT coefficient reconstructions without surrogates or pretraining.
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Self-Supervised Calibration of Scientific Instruments Using Physical Consistency Constraints
A physics-informed self-supervised framework learns detector calibration parameters and ionic charge-state predictions jointly from raw spectrometer data using iterative pseudo-labelling driven by physical constraints.
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Recovering Sharp Conductivity Features in the Finite-Data Calder\'on Problem with Physics-Informed Neural Networks
A PINN framework with separate networks for conductivity and potentials, multiscale wavelet excitations, and FFE recovers dominant conductivity structures from finite DtN data with 3-12% relative error on synthetic tests, with FFE aiding sharp features.
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Slay the Shear: A Unified Statistical Framework for Weak Gravitational Lensing Shear Estimation
Unified framework proves the score function yields the minimum-variance unbiased shear estimator and that response-weighted inverse-variance weights minimize shape noise independent of galaxy shape distributions, with RDSM reducing noise by ~17.5% at LSST depth.
-
A Neural Surrogate Approach for Simulating Natural Convection Problems
A Fourier neural operator trained on Boussinesq-compressible simulation pairs corrects Boussinesq predictions for natural convection, achieving SSIM near unity and MSE reductions of one to three orders of magnitude.
-
Swarm-Inspired Generation of Collective Behaviors in Graph Dynamical Systems
SIES learns generalizable local coupling operators via signed source-target attention for controllable synchronization in graph dynamical systems and applies the principle to heterophilous graph representation learning.
-
Enhancing Speckle Metrology with Diffusion Denoising in Photon-Starved Regimes
A hybrid pre-trained and experimentally fine-tuned diffusion model denoises speckle data, cutting RMSE by up to 72% in femtometre-scale wavelength sensing with an integrating sphere where standard methods fail.
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Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems
Hybrid neural-process model derives biokinetic parameters from genomic traits for soil organic matter turnover, with ecological constraints, and outperforms baselines on synthetic and real data.
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Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
QCPIKAN is a quantum-classical physics-informed KAN that claims exponential high-frequency error convergence and superior accuracy over prior QCPINNs on single-phase, transport, and two-phase seepage PDEs.
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Reconstructing Galactic Gravitational Potentials from Stellar Kinematics with Physics-Informed Neural Networks
A PINN approach learns galactic gravitational potentials from acceleration data, achieving sub-percent errors on simulations while outperforming analytic models and retaining interpretability via structured priors.
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A Diagnostic Software Suite for Auditing Learned PDE Simulators
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
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Self-Evolving Scientific Agent Discovers Generalizable Physically-Reasoned Fluid Control
An LLM-based self-evolving agent discovers a traveling-wave controller with body-frame guidance and yaw feedback that generalizes to unseen targets for an underactuated fluid swimmer.
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Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
Oscillatory state-space models with PDE-aware spectral bases are introduced as inductive biases for PINNs, yielding improved accuracy and lower memory on forward, inverse, and up to 100D PDE tasks.
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PIDM-DP: Physics-Informed Diffusion with Dormand-Prince Integration for Chaotic System Identification and State Reconstruction across Multiple Dynamical Regimes
PIDM-DP integrates Dormand-Prince ODE solving into DDPM denoising with scheduled physics guidance to reconstruct chaotic states, reporting up to 15.4x RMSE gains over baselines on five systems including stiff cases.
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Semigroup Consistency as a Diagnostic for Learned Physics Simulators
Normalized semigroup error is introduced as a diagnostic for learned simulators on 1D heat and Burgers equations; it correlates with rollout degradation (Spearman ρ=0.635) while regularization shows mixed results.
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AstroMind: A High-Fidelity Benchmark for Spacecraft Behavior Reasoning Based on Large Language Models
AstroMind is a new physics-grounded benchmark for LLM reasoning on spacecraft behavior across intent inference, maneuver estimation, and threat assessment, evaluated on several open-weight models.
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Learning partially observed systems with neural Hamiltonian ordinary differential equations
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
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Learning inelastic constitutive models from stress-strain data under hard thermodynamic constraints
A neural constitutive model with hard thermodynamic constraints learns inelastic stress-strain behavior from data and predicts unseen cyclic paths, including granular-media hysteresis.
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A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming
CAttBiGNN is a bipartite GNN with edge-aware cross attention that predicts coupled nodal displacements and elemental thinning for autoregressive rollout of explicit dynamic FE simulations on dome and corner forming benchmarks, outperforming node-centered baselines.
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Physics Guided Generative Optimization for Trotter Suzuki Decomposition
P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.
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PG-3DGS: Optimizing 3D Gaussian Splatting to Satisfy Physics Objectives
PG-3DGS couples 3D Gaussian Splatting with differentiable physics so that optimized shapes satisfy both visual fidelity and physical objectives such as pouring and aerodynamic lift, with real-world 3D-printed validation.
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ShardTensor: Domain Parallelism for Scientific Machine Learning
ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.
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Generalized Global Self-Optimizing Control for Chemical Processes: Part II Objective-Guided Controlled Variable Learning Approach
OGCVL integrates symbolic and numerical techniques to learn effective nonlinear controlled variables for scalable self-optimizing control in chemical processes.
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Estimation of Motor Unit Parameters from Surface Electromyograms using an Informed Autoencoder
An informed autoencoder estimates subject-specific motor unit parameters from surface EMG by reconstructing signals in a latent space that respects physical laws relating parameters to observed signals.
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Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocity
MuFiNNs integrates sparse experimental measurements with structured low-fidelity models via hierarchical construction and nonlinear correction to predict 3D flame wrinkling dynamics and turbulent mass burning velocity across fuels, pressures, and turbulence levels.
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A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
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Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems
A new scale-aware diagnostic framework shows that unconstrained diffusion generative models exhibit structural freezing and instability instead of smooth physical responses under multiscale perturbations.
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Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.
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Physics-Guided Tiny-Mamba Transformer for Reliability-Aware Early Fault Warning
PG-TMT couples a physics-aligned tri-branch encoder with EVT-calibrated decision rules to achieve higher PR-AUC and shorter detection times at controlled false-alarm rates across multiple bearing datasets.
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MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration
MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
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Empirical Calibration and Conditional-Reliability Diagnostics for Bearing RUL Prediction under Operating-Regime Shift
On a 10-bearing PHME subset, a residual-calibrated fusion model hits ~0.15 normalized MAE and 0.90 average 90% coverage under leave-regime-out splits, while conditional diagnostics expose 0.666 coverage and raw-channel-loss collapse.
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When the Timetable Breaks: Physics-Anchored Scientific Machine Learning for Cold-Wave-Robust Battery-Electric Bus Operations
WeatherRobustBus injects hourly weather into real bus blocks, couples a physics backbone with a bounded monotone residual ensemble, and shows a policy reducing cold-wave failure probability from 0.759 to 0.112.
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Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Controlled benchmarks on Burgers, Darcy, Allen-Cahn and Navier-Stokes problems show grid unknowns favor discrete adjoint while neural representations favor PINNs, with PINNs cheaper for time-dependent cases and a hybrid strategy recovering adjoint accuracy at lower cost.
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Bayesian Optimization of a Multi-Product Chemical Reactor Using Composite Models and Partial Physics Knowledge
Composite Gaussian process models with an analytical profit function and a steady-state energy-balance residual are embedded in Bayesian optimization to improve economic performance and constraint satisfaction on a simulated multi-product chemical reactor.
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DN-Hypo-Pipeline: An AI-Driven Workflow for Generating Hypotheses using Large Language Models and Scientific Explanations
Structuring LLM hypothesis generation around deductive-nomological explanation, causal processes, and universals is reported to beat direct prompting, with two generated ideas implemented as the CTAT and HALO algorithms.
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A Systematic Benchmark of Physics-Informed Neural Network Architectures for the Stiff Poisson-Nernst-Planck System: Adaptive LossWeighting and Multi-Scale Resolution
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.
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Striding Across Reynolds Numbers: Representation Geometry in Neural PDE Generalisation
ConvAE-Relay retrieval via source-trained autoencoder latent matching achieves 38.34+/-0.07% relative L2 error on 10x Re shift using only source database, with U-Net at 34.72% and matching quality identified as dominant factor.
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Overcoming "Physics Shock" in Earth Observation A Heteroscedastic Uncertainty Framework for PINN-based Flood Inference
A heteroscedastic uncertainty PINN with warm-start and deep ensembles for SAR flood inference claims 25% IoU gain by relaxing physics constraints in high-noise regions.