Pith. sign in

REVIEW 3 major objections 6 minor 51 references

Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read By replacing a discontinuous external signal with a sequence of smooth neural-network surrogates, HADES-NN turns a nonsmooth parameter-estimation problem into smooth ones whose minimizers converge to the true minimum, recovering accurate…

desk verdict HADES-NN is a practical, well-demonstrated estimation method for ODEs with discontinuous inputs, but its convergence proof has real gaps and shouldn't be taken as established. read the letter →

arxiv 2507.06267 v1 pith:REPBLPO6 submitted 2025-07-08 cs.LG

Hyeontae Jo , Krešimir Josić , Jae Kyoung Kim This is my paper · ORCID
classification cs.LG MSC 34C6092B0568T0793C1565K10
keywords non-autonomousdifferentialequationsdiscontinuousexternalsignalsneuralnetworksmoothingparameterestimationLevenberg-MarquardtnonsmoothoptimizationcircadianclockLotka-Volterramodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Fitting a non-autonomous differential equation becomes hard when the external input changes abruptly, because the loss landscape is nonsmooth and standard optimizers stall. The paper's claim is that this difficulty can be bypassed by smoothing: HADES-NN (Harmonic Approximation of Discontinuous External Signals using Neural Networks) uses a neural network with cosine and smooth hidden activations to produce a sequence of smooth approximations $\tilde S_n(t)$ to the discontinuous signal $S(t)$, and a least-squares optimizer fits the parameters $\vec p_n$ to each smoothed model. The paper proves that the minimizers of these smoothed loss functions converge to the minimizer of the original nonsmooth loss as the approximations improve. On a Lotka-Volterra system, a human circadian pacemaker driven by wearable light data, and a yeast mating-response network, HADES-NN recovers accurate parameter estimates where L-BFGS, SLSQP, LM, Nelder-Mead, differential evolution, and NeuralODE do not. The payoff would be a general and computationally cheap route to fitting realistic models whose inputs change abruptly.

What carries the argument

The load-bearing object is the iterated surrogate loss. Instead of minimizing the nonsmooth loss $\|\vec y_{\mathrm{obs}} - \vec y(\cdot,\vec p,S)\|$ directly, HADES-NN minimizes $\|\vec y_{\mathrm{obs}} - \vec y(\cdot,\vec p,\tilde S_n)\|$ for a neural-network-smoothed input $\tilde S_n(t)$, then uses the resulting $\vec p_n$ to warm-start the next round of smoothing and fitting. Four ingredients carry the proof: the network architecture makes $\tilde S_n(t)$ smooth; sensitivity equations make the surrogate loss differentiable in $\vec p$; a Levenberg-Marquardt convergence bound makes each smooth subproblem solvable; and a Grönwall-type inequality shows trajectory differences are bounded by input differences, so surrogate minima approach the true minimum.

What would settle it

On the circadian benchmark, fix the smoothed signal from a late HADES-NN iteration and exhaustively search the four-parameter box for the global minimum of that smoothed loss; if the warm-started Levenberg-Marquardt estimate is not that global minimum, the proof's central premise fails even if the final estimates look accurate.

Watch

Extended reading notes

Core claim

The central discovery is that the nonsmooth optimization problem caused by a discontinuous input $S(t)$ can be replaced by a sequence of smooth problems that carry the same global minimum. HADES-NN does this in two iterated stages: a fully connected network with a cosine signal layer and five hidden layers of Exponential Linear Units approximates $S(t)$ by a smooth $\tilde S_n(t)$, and a Levenberg-Marquardt least-squares fit estimates $\vec p_n$ for the model driven by $\tilde S_n(t)$. The sequence $\vec p_n$ converges to the minimizer of the original loss; the proof combines differentiability of each smoothed loss, solvability of each smoothed subproblem, and a Grönwall-type stability bound showing that close signal approximations give close trajectories. In the paper's benchmarks, the method recovered the true parameters of the Lotka-Volterra, circadian, and yeast models, and was the only tested method to do so reliably in the circadian case.

Load-bearing premise

The load-bearing premise is that at every iteration the least-squares optimizer actually finds the global minimum of the smoothed model, and that successive smoothed minimizers stay in a bounded region where close loss values force close parameters; if either assumption fails, the proof no longer supports the claimed convergence.

Editorial extensions

If this is right

  • With 20 or more observations from the switching Lotka-Volterra system, HADES-NN and NeuralODE both approach the true parameters, and HADES-NN has the smaller mean absolute percentage error.
  • In the circadian pacemaker benchmark with a wearable light signal, only HADES-NN among the seven tested methods reliably recovers the four individual-specific parameters.
  • In the yeast mating-response network with 23 parameters, HADES-NN narrows the estimated parameter ranges relative to the original evolutionary-algorithm study while matching the experimental GFP trajectories.
  • The convergence theorem implies that improving the signal approximation directly improves parameter accuracy, so collecting more signal observations should help as well as more state observations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Inference: the same alternating smoothing-and-fitting scheme should transfer to any abruptly changing input that can be approximated in $L^2$, such as on-off drug dosing, electrical switching, or sudden policy changes, without changing the core machinery.
  • Inference: because each iteration yields a point estimate, the sequence of iterates could be interpreted as an empirical distribution for uncertainty quantification, an extension the paper mentions only in passing.
  • Inference: the proof's reliance on universal approximation suggests the guarantee should extend beyond step-like Markov signals to a broad class of discontinuous inputs with finite $L^2$ norm; this is a testable prediction.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes HADES-NN, an iterative two-stage method for estimating parameters of non-autonomous ODEs with discontinuous external signals. Stage 1 fits a smooth neural-network approximation of the discontinuous signal; Stage 2 uses this smooth signal in the ODE and estimates parameters with Levenberg-Marquardt. The two stages are alternated and warm-started from the previous iteration. The method is demonstrated on a Lotka-Volterra model with a Markov-switching input, a human circadian pacemaker model driven by wearable light-exposure data, and a yeast mating-response network with experimental data. The paper also states and proves a convergence theorem in Appendix B claiming that the sequence of parameter estimates converges to the minimizer of the original non-smooth loss.

Significance. If the theoretical claim and numerical comparisons hold, HADES-NN would be a practically useful and conceptually simple solution to a real obstacle in fitting non-autonomous models with abrupt inputs: the non-smoothness of the loss landscape that defeats standard gradient-based and direct-search optimizers. The paper's strengths are its breadth of applications, the use of experimentally measured input signals and data in the circadian and yeast examples, and the systematic comparison with six alternative optimizers across 100 random initializations. The numerical demonstrations are internally consistent and show a clear practical effect. However, the central convergence proof in Appendix B has a genuine gap concerning the global-optimality assumption on the LM stage, and the final step from loss convergence to parameter convergence is not justified by the stated assumptions. These issues do not invalidate the empirical contribution, but they do mean the headline theoretical guarantee is not established as written.

major comments (3)
  1. [Appendix B, Theorem B.4; Section 3.2, Eq. (3.5)] Theorem B.4 assumes that p_n is a global minimizer of the smooth surrogate loss (3.5), but the implemented Stage 2 uses the Levenberg-Marquardt algorithm, which is a local method. Proposition B.2, cited from Ref. [49], only guarantees that a stationary point with gradient norm below tolerance is reached within O(eps^{-2}) iterations; it does not establish that p_n equals argmin of (3.5) in a nonconvex landscape. The first inequality in the proof of Theorem B.4 relies exactly on p_n being a global minimizer, so the proof does not cover the algorithm as implemented. The authors should either add conditions under which LM finds the global minimum, verify global optimality numerically for the reported examples, or weaken the theorem and adjust the claims in the abstract and introduction accordingly.
  2. [Appendix B, Theorem B.4, final paragraph] The proof moves from convergence of the surrogate loss values to convergence of the parameter vectors, but this step is not justified. From lim_n ||y_obs - y(.; p_n, S_tilde_n)|| <= ||y_obs - y(.; p*, S)|| one cannot conclude p_n -> p* unless {p_n} is known to lie in a compact set and the true loss is continuous in p (or some equivalent identifiability-plus-compactness condition holds). Assumption 1 (uniqueness of p*) alone does not provide compactness. Moreover, the displayed inequality bounds the surrogate loss with S_tilde_n, not the true loss with S; an additional triangle-inequality step is needed before loss convergence can be related to parameter convergence. Please state and verify the missing compactness and continuity assumptions.
  3. [Section 3.2 and Appendix B, Theorem B.4] The proof of Theorem B.4 assumes ||S_tilde_n - S||_{L2({t^o_j})} < eps for the observation times, but Stage 1 trains the network to match S at the signal-observation times {t^s_i} using Eq. (3.3). The manuscript does not state that {t^o_j} is contained in {t^s_i}, nor does it provide an argument transferring L2 convergence from one finite grid to another. This is a missing hypothesis in the convergence theorem and should be stated explicitly or proved.
minor comments (6)
  1. [Section 2.2] The paragraph beginning 'We compared the performance of HADES-NN with six popular optimization algorithms' appears twice verbatim; please remove the duplicate.
  2. [Proposition B.1] There are typos in this proposition: 'respoect' should be 'respect' and 'dependnt' should be 'dependent'.
  3. [Lemma B.3, Eq. (14)] In inequality (14), the constant C2 from the Lipschitz-in-S assumption appears in a term that bounds the difference F(y1,p,S2) - F(y2,p,S2); this term should involve the Lipschitz constant C1 for y (or a generic constant C(T)). This does not affect the argument because the constants are generic, but the displayed formula is misleading.
  4. [Appendix B, Theorem B.4] The proof mixes the notations S_tilde_n and S_n for the same smooth approximation; please use one notation consistently.
  5. [Eq. (3.2)] The displayed formula for the loss function contains apparent typesetting artifacts with extra parentheses and a misplaced backslash; please fix the LaTeX so that the L2 norm notation is unambiguous.
  6. [General] No code or data availability statement is included. Given that the method is computational and the yeast and circadian examples use real data, a statement on code and data availability would substantially aid reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: HADES-NN's estimates are validated against ground-truth parameters in synthetic data and experimental trajectories; self-citations appear only in non-load-bearing related-work discussion.

full rationale

The central claim of the paper is that iterating between a neural-network smoothing step and a Levenberg-Marquardt parameter-estimation step yields estimates converging to the minimizer of the original non-smooth loss. Each stage's input is distinct from the output being claimed: the signal approximation S_n(t) is trained to the observed signal S(t) via Eq. (3.3), and the parameter estimate p_n is obtained by fitting the ODE with S_n to the observed y data via Eq. (3.5). The convergence proof in Appendix B uses standard ingredients: a universal approximation result [51] for S_n -> S, a Gronwall-type stability estimate (Lemma B.3), and the defining property that p_n is a global minimizer of the smoothed loss. The first inequality in Theorem B.4 'follows from the definition of the global optimum' — this is a legitimate use of the algorithm's own defining equation, not a circular reduction, because p_n is not assumed equal to p* but is characterized as minimizing a different, smoothed loss. The proof does contain a genuine gap: Step 2 claims LM reaches the global minimizer of Eq. (3.5), but the cited Proposition B.2 only guarantees reaching a stationary point, and the final inference from loss convergence to parameter convergence lacks a compactness/continuity argument. These are missing derivation steps or incorrect citation claims, not self-referential reductions. The self-citations (Refs. [43-46]) appear only in the Discussion when surveying PINN-based parameter estimation and are not used to justify any premise of HADES-NN's correctness. The method is benchmarked against ground truth in synthetic Lotka-Volterra and circadian examples and against experimental GFP trajectories in the yeast example, so the reported accuracy is independent evidence rather than a consequence of how inputs were constructed.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central derivation rests on the surrogate loss being globally minimized by LM at every iteration, on universal approximation of the discontinuous signal by the trained network, and on identifiability and Lipschitz assumptions that are stated but not verified. The network architecture (16 nodes, 5 hidden layers, cosine then ELU activations) and the stopping tolerance are hand-chosen and not ablated. No new entities are introduced; the method is a numerical scheme rather than a new physical object.

free parameters (2)
  • Neural network architecture: 1 cosine layer of 16 nodes, 5 hidden layers of 16 ELU nodes, 1 output node
    Chosen by hand (Section 3.2) without an ablation study; performance of the smooth approximation S_n likely depends on these choices, and training hyperparameters (learning rate, epochs) are unreported.
  • Stopping tolerance epsilon in Eq. (3.6) = not reported numerically
    Controls when the outer loop stops and therefore the final estimate; its value is not given, which hurts reproducibility.
assumptions (6)
  • standard math Existence of neural networks approximating S in L2 (universal approximation, Ref [51])
    Invoked in Theorem B.4 for S_n to S; standard for continuous targets and plausible for discontinuous ones in L2, though the rate is not controlled.
  • domain assumption The trained HADES network actually achieves the required approximation accuracy at each outer-loop iteration
    The proof assumes ||S_n - S||_L2 < epsilon for large n, but training with SGD gives no such guarantee; empirical convergence is shown for the examples, not proven.
  • domain assumption Assumption 1: the true loss has a unique minimizer p* (identifiability)
    Required in the last step of Theorem B.4; not verified for the circadian or yeast models.
  • domain assumption Assumption 2: F is Lipschitz in y and S
    Used in Lemma B.3; plausible for the examples but not checked; the circadian model includes terms that may not be globally Lipschitz.
  • ad hoc to paper LM solves the surrogate loss to global optimality at each iteration
    Step 2 of Appendix B claims LM reaches the global minimizer p_n; the cited result [49] gives an iteration bound to a stationary point under inverse-problem assumptions, not global optimality of a nonconvex loss. The whole convergence argument depends on this.
  • domain assumption The numerical ODE solver's solution matches the exact solution closely enough that the smoothness theory applies
    The motivation (non-smooth loss) comes from numerical integration of discontinuous ODEs, while Lemma B.3 and Theorem B.4 treat exact solutions; the paper does not analyze solver-induced non-smoothness.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals." pith.science (2026). https://pith.science/paper/REPBLPO6

@misc{pith2026250706267,
  author       = {Pith},
  title        = {Pith review of: Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/REPBLPO6}},
  note         = {Machine review of arXiv:2507.06267}
}
read the original abstract

Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a novel parameter estimation method utilizing functional approximations with artificial neural networks. Our approach, termed Harmonic Approximation of Discontinuous External Signals using Neural Networks (HADES-NN), operates in two iterated stages. In the first stage, the algorithm employs a neural network to approximate the discontinuous signal with a smooth function. In the second stage, it uses this smooth approximate signal to estimate model parameters. HADES-NN gives highly accurate and precise parameter estimates across various applications, including circadian clock systems regulated by external light inputs measured via wearable devices and the mating response of yeast to external pheromone signals. HADES-NN greatly extends the range of model systems that can be fit to real-world measurements.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

51 extracted references · 48 canonical work pages

  1. [49]

    Convergence and complexity analysis of a levenberg–marquardt algorithm for inverse problems

    El Houcine Bergou, Youssef Diouane, and Vyacheslav Kungurtsev. Convergence and complexity analysis of a levenberg–marquardt algorithm for inverse problems. Journal of Optimization Theory and Applications , 185:927–944, 2020

    work page 2020

  2. [1]

    Evolution-informed forecasting of seasonal influenza a (h3n2)

    Xiangjun Du, Aaron A King, Robert J Woods, and Mercedes Pascual. Evolution-informed forecasting of seasonal influenza a (h3n2). Science translational medicine, 9(413):eaan5325, 2017

    work page 2017

  3. [2]

    Vaccination of dogs in an african city interrupts rabies transmission and reduces human exposure

    Jakob Zinsstag, Monique Lechenne, Mirjam Laager, Rolande Mindekem, Service Na ¨ ıssengar, Assandi Oussiguere, Kebkiba Bidjeh, Germain Rives, Julie Tessier, Seraphin Madjaninan, et al. Vaccination of dogs in an african city interrupts rabies transmission and reduces human exposure. Science translational medicine, 9(421):eaaf6984, 2017

    work page 2017

  4. [3]

    Measuring competitive exclusion in non–small cell lung cancer

    Nathan Farrokhian, Jeff Maltas, Mina Dinh, Arda Durmaz, Patrick Ellsworth, Masahiro Hit- omi, Erin McClure, Andriy Marusyk, Artem Kaznatcheev, and Jacob G Scott. Measuring competitive exclusion in non–small cell lung cancer. Science Advances, 8(26):eabm7212, 2022

    work page 2022

  5. [4]

    A simpler model of the human circadian pacemaker

    Daniel B Forger, Megan E Jewett, and Richard E Kronauer. A simpler model of the human circadian pacemaker. Journal of biological rhythms , 14(6):533–538, 1999

    work page 1999

  6. [5]

    Enhanced circadian phase tracking: A 5-h dlmo sampling protocol using wearable data

    Dongju Lim, Su Jung Choi, Yun Min Song, Hea Ree Park, Eun Yeon Joo, and Jae Kyoung Kim. Enhanced circadian phase tracking: A 5-h dlmo sampling protocol using wearable data. Journal of Biological Rhythms , 40(3):249–261, 2025

    work page 2025

  7. [6]

    A predictive model of gene expression reveals the role of network motifs in the mating response of yeast

    Amy E Pomeroy, Matthew I Pena, John R Houser, Gauri Dixit, Henrik G Dohlman, Timothy C Elston, and Beverly Errede. A predictive model of gene expression reveals the role of network motifs in the mating response of yeast. Science signaling, 14(670):eabb5235, 2021

    work page 2021

  8. [7]

    Parameter estimation of power elec- tronic converters with physics-informed machine learning

    Shuai Zhao, Yingzhou Peng, Yi Zhang, and Huai Wang. Parameter estimation of power elec- tronic converters with physics-informed machine learning. IEEE Transactions on Power Electronics, 37(10):11567–11578, 2022

    work page 2022

Show all 51 references
  1. [8]

    Differentially private sgd with non- smooth losses

    Puyu Wang, Yunwen Lei, Yiming Ying, and Hai Zhang. Differentially private sgd with non- smooth losses. Applied and Computational Harmonic Analysis , 56:306–336, 2022

    2022

  2. [9]

    A software package for sequential quadratic programming

    Dieter Kraft. A software package for sequential quadratic programming. Forschungsbericht- Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt , 1988

    1988

  3. [10]

    Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization

    Ciyou Zhu, Richard H Byrd, Peihuang Lu, and Jorge Nocedal. Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization. ACM Transactions on mathematical software (TOMS) , 23(4):550–560, 1997

    1997

  4. [11]

    The levenberg-marquardt algorithm: implementation and theory

    Jorge J Mor´ e. The levenberg-marquardt algorithm: implementation and theory. In Numerical analysis: proceedings of the biennial Conference held at Dundee, June 28–July 1, 1977 , pages 105–116. Springer, 2006

    1977

  5. [12]

    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

  6. [13]

    Implementing the nelder-mead simplex algorithm with adaptive parameters

    Fuchang Gao and Lixing Han. Implementing the nelder-mead simplex algorithm with adaptive parameters. Computational Optimization and Applications , 51(1):259–277, 2012

    2012

  7. [14]

    Differential evolution: a practical approach to global optimization

    Kenneth Price, Rainer M Storn, and Jouni A Lampinen. Differential evolution: a practical approach to global optimization . Springer Science & Business Media, 2006

    2006

  8. [15]

    Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization

    R Garmanjani and LN Vicente. Smoothing and worst-case complexity for direct-search methods in nonsmooth optimization. IMA Journal of Numerical Analysis , 33(3):1008–1028, 2013

    2013

  9. [16]

    Linearly constrained nonsmooth and nonconvex minimization

    Marco Artina, Massimo Fornasier, and Francesco Solombrino. Linearly constrained nonsmooth and nonconvex minimization. SIAM Journal on Optimization , 23(3):1904–1937, 2013

    1904

  10. [17]

    The admm-pinns algorithmic framework for nonsmooth pde-constrained optimization: a deep learning approach

    Yongcun Song, Xiaoming Yuan, and Hangrui Yue. The admm-pinns algorithmic framework for nonsmooth pde-constrained optimization: a deep learning approach. SIAM Journal on Scientific Computing , 46(6):C659–C687, 2024

    2024

  11. [18]

    Deep neural networks learn non-smooth functions effectively

    Masaaki Imaizumi and Kenji Fukumizu. Deep neural networks learn non-smooth functions effectively. In The 22nd international conference on artificial intelligence and statistics , pages 869–878. PMLR, 2019

    2019

  12. [19]

    The gap between theory and practice in function approximation with deep neural networks

    Ben Adcock and Nick Dexter. The gap between theory and practice in function approximation with deep neural networks. SIAM Journal on Mathematics of Data Science , 3(2):624–655, 2021

    2021

  13. [20]

    Numerical methods for optimal control with binary control functions applied to a lotka- volterra type fishing problem

    Sebastian Sager, Hans Georg Bock, Moritz Diehl, Gerhard Reinelt, and Johannes P Schloder. Numerical methods for optimal control with binary control functions applied to a lotka- volterra type fishing problem. In Recent Advances in Optimization , pages 269–289. Springer, 2006

    2006

  14. [21]

    Bolt-on differential privacy for scalable stochastic gradient descent-based analytics

    Xi Wu, Fengan Li, Arun Kumar, Kamalika Chaudhuri, Somesh Jha, and Jeffrey Naughton. Bolt-on differential privacy for scalable stochastic gradient descent-based analytics. In Proceedings of the 2017 ACM International Conference on Management of Data , pages 1307–1322, 2017

    2017

  15. [22]

    Raef Bassily, Vitaly Feldman, Kunal Talwar, and Abhradeep Guha Thakurta. Private stochas- This manuscript has been submitted to SIAM Journal on Applied Mathematics PARAMETER ESTIMATION OF SYSTEMS WITH ABRUPT SIGNAL 19 tic convex optimization with optimal rates. Advances in neu...

    2019

  16. [23]

    Private stochastic convex optimization: optimal rates in linear time

    Vitaly Feldman, Tomer Koren, and Kunal Talwar. Private stochastic convex optimization: optimal rates in linear time. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing , pages 439–449, 2020

    2020

  17. [24]

    Stability of stochastic gradient descent on nonsmooth convex losses

    Raef Bassily, Vitaly Feldman, Crist´ obal Guzm´ an, and Kunal Talwar. Stability of stochastic gradient descent on nonsmooth convex losses. Advances in Neural Information Processing Systems, 33:4381–4391, 2020

    2020

  18. [25]

    The effects of self-selected light-dark cycles and social constraints on human sleep and circadian timing: a modeling approach

    Anne C Skeldon, Andrew JK Phillips, and Derk-Jan Dijk. The effects of self-selected light-dark cycles and social constraints on human sleep and circadian timing: a modeling approach. Scientific reports, 7(1):45158, 2017

    2017

  19. [26]

    Optimal adjust- ment of the human circadian clock in the real world

    Samuel Christensen, Yitong Huang, Olivia J Walch, and Daniel B Forger. Optimal adjust- ment of the human circadian clock in the real world. PLOS Computational Biology , 16(12):e1008445, 2020

    2020

  20. [27]

    Predicting circadian misalignment with wearable technology: validation of wrist- worn actigraphy and photometry in night shift workers

    Philip Cheng, Olivia Walch, Yitong Huang, Caleb Mayer, Chaewon Sagong, Andrea Cua- matzi Castelan, Helen J Burgess, Thomas Roth, Daniel B Forger, and Christopher L Drake. Predicting circadian misalignment with wearable technology: validation of wrist- worn actigraphy and photo...

    2021

  21. [28]

    Predicting circadian phase across populations: a comparison of mathematical models and wearable devices

    Yitong Huang, Caleb Mayer, Philip Cheng, Alankrita Siddula, Helen J Burgess, Christopher Drake, Cathy Goldstein, Olivia Walch, and Daniel B Forger. Predicting circadian phase across populations: a comparison of mathematical models and wearable devices. Sleep, 44(10):zsab126, 2021

    2021

  22. [29]

    Personalized sleep-wake patterns aligned with circadian rhythm relieve daytime sleepiness

    Jaehyoung Hong, Su Jung Choi, Se Ho Park, Hyukpyo Hong, Victoria Booth, Eun Yeon Joo, and Jae Kyoung Kim. Personalized sleep-wake patterns aligned with circadian rhythm relieve daytime sleepiness. Iscience, 24(10), 2021

    2021

  23. [30]

    A real-time, personalized sleep intervention using mathematical modeling and wearable devices

    Yun Min Song, Su Jung Choi, Se Ho Park, Soo Jin Lee, Eun Yeon Joo, and Jae Kyoung Kim. A real-time, personalized sleep intervention using mathematical modeling and wearable devices. Sleep, 46(9):zsad179, 2023

    2023

  24. [31]

    A digital, real-time, history-based sleep- management tool to enhance alertness

    Yun Min Song, Su Jung Choi, Dongju Lim, Reinatt Hansel Wijaya, Hyeong Jun Jang, Hea Ree Park, Eun Yeon Joo, and Jae Kyoung Kim. A digital, real-time, history-based sleep- management tool to enhance alertness. Sleep, page zsaf160, 2025

    2025

  25. [32]

    Model-based hu- man circadian phase estimation using a particle filter

    Christopher Mott, Guy Dumont, Diane B Boivin, and Daniel Mollicone. Model-based hu- man circadian phase estimation using a particle filter. IEEE Transactions on Biomedical Engineering, 58(5):1325–1336, 2011

    2011

  26. [33]

    Parameter estimation in a model of the human circadian pacemaker using a particle filter

    Jochem Bonarius, Charikleia Papatsimpa, and Jean-Paul Linnartz. Parameter estimation in a model of the human circadian pacemaker using a particle filter. IEEE Transactions on Biomedical Engineering, 68(4):1305–1316, 2020

    2020

  27. [34]

    The role of light sensitivity and intrinsic circadian period in predicting individual circadian timing

    Julia E Stone, Elise M McGlashan, Nina Quin, Kayan Skinner, Jessica J Stephenson, Sean W Cain, and Andrew JK Phillips. The role of light sensitivity and intrinsic circadian period in predicting individual circadian timing. Journal of Biological Rhythms , 35(6):628–640, 2020

    2020

  28. [35]

    Extracting circadian and sleep parameters from longitudinal data in schizophrenia for the design of pragmatic light interventions

    Anne C Skeldon, Derk-Jan Dijk, Nicholas Meyer, and Katharina Wulff. Extracting circadian and sleep parameters from longitudinal data in schizophrenia for the design of pragmatic light interventions. Schizophrenia Bulletin , 48(2):447–456, 2022

    2022

  29. [36]

    Anne C Skeldon, Thalia Rodriguez Garcia, Sean F Cleator, Ciro della Monica, Kiran KG Ravin- dran, Victoria L Revell, and Derk-Jan Dijk. Method to determine whether sleep pheno- types are driven by endogenous circadian rhythmicity or environmental light by combining longitudina...

    2023

  30. [37]

    Implicit neural representations with periodic activation functions

    Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33:7462–7473, 2020

    2020

  31. [38]

    Fourier features let networks learn high frequency functions in low dimensional domains

    Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng. Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Proc...

    2020

  32. [39]

    Shallow univariate relu networks as splines: initialization, loss surface, hessian, and gradient flow dynamics

    Justin Sahs, Ryan Pyle, Aneel Damaraju, Josue Ortega Caro, Onur Tavaslioglu, Andy Lu, Fabio Anselmi, and Ankit B Patel. Shallow univariate relu networks as splines: initialization, loss surface, hessian, and gradient flow dynamics. Frontiers in artificial intelligence , 5:889981, 2022

    2022

  33. [40]

    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. This manusc...

    2019

  34. [41]

    Characterizing possible failure modes in physics-informed neural networks

    Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert Kirby, and Michael W Mahoney. Characterizing possible failure modes in physics-informed neural networks. Advances in Neural Information Processing Systems , 34:26548–26560, 2021

    2021

  35. [42]

    Physics-informed machine learning

    George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics-informed machine learning. Nature Reviews Physics , 3(6):422–440, 2021

    2021

  36. [43]

    Deep neural network approach to forward-inverse problems

    Hyeontae Jo, Hwijae Son, Hyung Ju Hwang, and Eunheui Kim. Deep neural network approach to forward-inverse problems. arXiv preprint arXiv:1907.12925 , 2019

    1907 arXiv

  37. [44]

    Trend to equilibrium for the kinetic fokker-planck equation via the neural network approach

    Hyung Ju Hwang, Jin Woo Jang, Hyeontae Jo, and Jae Yong Lee. Trend to equilibrium for the kinetic fokker-planck equation via the neural network approach. Journal of Computational Physics, 419:109665, 2020

    2020

  38. [45]

    Real-world implications of a rapidly responsive covid-19 spread model with time-dependent parameters via deep learn- ing: Model development and validation

    Se Young Jung, Hyeontae Jo, Hwijae Son, and Hyung Ju Hwang. Real-world implications of a rapidly responsive covid-19 spread model with time-dependent parameters via deep learn- ing: Model development and validation. Journal of medical Internet research, 22(9):e19907, 2020

    2020

  39. [46]

    Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction

    Hyeontae Jo, Hyukpyo Hong, Hyung Ju Hwang, Won Chang, and Jae Kyoung Kim. Density physics-informed neural networks reveal sources of cell heterogeneity in signal transduction. Patterns, 5(2), 2024

    2024

  40. [47]

    Sensitivity analysis of ordinary differential equation systems—a direct method

    Robert P Dickinson and Robert J Gelinas. Sensitivity analysis of ordinary differential equation systems—a direct method. Journal of computational physics , 21(2):123–143, 1976

    1976

  41. [48]

    Principles of discontinuous dynamical systems

    Marat Akhmet. Principles of discontinuous dynamical systems . Springer Science & Business Media, 2010

    2010

  42. [50]

    A generalized gronwall inequality and its application to a fractional differential equation

    Haiping Ye, Jianming Gao, and Yongsheng Ding. A generalized gronwall inequality and its application to a fractional differential equation. Journal of Mathematical Analysis and Applications, 328(2):1075–1081, 2007

    2007

  43. [51]

    Minimum width for universal approxi- mation

    Sejun Park, Chulhee Yun, Jaeho Lee, and Jinwoo Shin. Minimum width for universal approxi- mation. arXiv preprint arXiv:2006.08859 , 2020. This manuscript has been submitted to SIAM Journal on Applied Mathematics

    2006 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.