Pith. sign in

REVIEW 5 major objections 6 minor 37 references

EpiNode, a decomposition-controlled neural ODE plus SIRS model, claims the best long-horizon epidemic forecasts and time-varying parameter recovery across five datasets, with RMSE reductions of 27–70% over the strongest baseline.

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 ↗

T0 review · deepseek-v4-flash

2026-08-03 03:55 UTC pith:BSE542WK

load-bearing objection Useful failure-mode catalog and a plausible architecture, but the inference-time control signal is either leaky or undefined—empirical claims don't hold as written. the 5 major comments →

arxiv 2602.06323 v2 pith:BSE542WK submitted 2026-02-06 cs.LG

How (Not) to Hybridize Neural and Mechanistic Models for Epidemiological Forecasting

Yiqi Su , Ray Lee , Jiaming Cui , Naren Ramakrishnan This is my paper
classification cs.LG MSC 92D3068T0737N25
keywords epidemic forecastingneural ODEsmechanistic compartmental modelspartial observabilityvariational mode decompositiontime-varying parametersSIRS model
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 paper argues that hybrid neural–mechanistic epidemic models fail under partial observability and shifting transmission dynamics unless non-stationarity is made explicit. It proposes EpiNode, which decomposes the observed infection curve into trend, seasonal, and residual components, uses those components as control signals for latent neural ODEs, and pipes decoded time-varying rates into a mechanistic SIRS model. The claim is that this decomposition-controlled coupling yields the lowest long-horizon RMSE across five datasets, with a 27–70% reduction over the strongest baseline, plus better peak timing, peak magnitude, and recovery of time-varying parameters, using only infection counts. If right, it means stable long-horizon epidemic forecasting and interpretable parameter inference are possible from partial surveillance data without auxiliary covariates.

Core claim

EpiNode's central claim is that making non-stationarity explicit fixes the failure modes of naive hybrids. Instead of feeding raw infections to a neural ODE or adding physics losses, it first decomposes I(t) via Variational Mode Decomposition into trend T(t), seasonal S(t), and residual N(t); each component drives its own latent ODE with time-delay embedding. The fused latent state decodes bounded time-varying transmission, recovery, and immunity-loss rates, and the SIRS equations roll the epidemic forward. The paper argues this structure anchors the latent state, prevents drift in unobserved compartments, stabilizes long-horizon rollouts, and lets the model recover parameters within ground-

What carries the argument

The load-bearing object is the trend–seasonal–residual decomposition of the single observed series, obtained by Variational Mode Decomposition, a variational method that separates the signal into band-limited modes around learned center frequencies. These components act as interpretable control signals for three collaborated latent neural ODEs whose states are fused and decoded into bounded time-varying SIRS parameters. The SIRS equations then propagate the epidemic state, enforcing epidemiological plausibility while the controls carry the non-stationarity.

Load-bearing premise

The load-bearing premise is that the trend, seasonal, and residual control signals extracted from the observed infection series are available or can be extrapolated for the forecast period; if they are computed from future data, the forecast is not causal, and the reported long-horizon accuracy would not transfer to real-time use.

What would settle it

Compute VMD only on the training portion of each benchmark, define a fixed extrapolation rule for the modes, and rerun the long-horizon evaluation; if RMSE jumps materially or rollouts collapse relative to the reported numbers, the central forecasting claim depends on non-causal access to the full series.

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

If this is right

  • If correct, infection-only surveillance data are sufficient for stable long-horizon forecasts, as long as the multi-scale structure is made explicit.
  • Time-varying beta, gamma, and delta can be recovered in interpretable bounded ranges, supporting retrospective analysis of epidemic drivers.
  • Peak timing and magnitude errors improve by 1–3 weeks and up to 30% relative to neural ODE and physics-informed baselines in the paper's experiments.
  • Disentangling components into separate latent ODEs and using VMD contributes the gains; ablations show three components beat one or two, and VMD beats MA, STL, wavelet, SSA–VMD, and Koopman variants on most datasets.
  • The method's gains are clearest when epidemic dynamics are structurally regular; the paper reports under-prediction for regions with abrupt post-split surges.

Where Pith is reading between the lines

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

  • The paper does not specify how the VMD control signals are produced for t beyond the split; Algorithm 1 decomposes the full series, so if the decomposition is run on the whole sequence, future observations leak into the controls and the forecast is not causal as written.
  • A fully causal version would require forecasting the modes themselves; quantifying the drop when modes are extrapolated from training data only would separate the value of the mechanistic coupling from access to future signal structure.
  • The method's edge likely depends on the regularity of epidemic dynamics; the hardest test would be a novel pathogen with sharp behavioral shifts outside the training window.

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

5 major / 6 minor

Summary. The paper proposes EpiNode, a hybrid neural-ODE + SIRS forecaster for epidemic time series. The observed infection curve is decomposed with Variational Mode Decomposition (VMD) into trend, seasonal, and residual components; these act as control signals for three latent Neural ODEs. The fused latent state is decoded into time-varying SIRS parameters, and the SIRS equations are rolled out to produce forecasts and parameter trajectories. The paper also catalogs failure modes of neural/mechanistic hybrids under partial observability and reports experiments on synthetic and real data (SIRS variants, SIR, SEIRS, ILI, and CLS) to support claims of improved RMSE, peak detection, and parameter recovery.

Significance. If EpiNode's forecasting mechanism were causally well-defined and the empirical results were internally consistent, the core idea—explicitly extracting multi-scale structure and using it as control inputs for a hybrid mechanistic/neural ODE—would be a timely and useful contribution. The paper's failure-mode catalog is instructive, and the release of code and a relatively clean architecture are positive aspects. However, as written, the forecasting protocol is not causal and the main quantitative claims are unsupported; the contribution cannot be assessed reliably.

major comments (5)
  1. [Appendix B, Algorithm 1; Section 3] Algorithm 1 decomposes the full observed series {I_i}_{i=0}^{T-1} via VMD at line 1, before any train/forecast split, and the loop over i=0..T-1 uses the resulting controls for both training and forecast indices. VMD is a global, non-causal transform; the controls for t>=t_split therefore depend on the very future observations the model is supposed to predict. Restricting the loss (17) to i<t_split does not prevent leakage because the forecast states are produced from future-derived controls. If instead the authors intend to decompose only training data, no extrapolation rule for continuing the trend/seasonal/residual controls beyond t_split is given; the statement in Appendix B that 'the learned model is rolled out beyond the observation window' is not a rule. Either way, the long-horizon forecasting claim is unsupported.
  2. [Abstract vs. Section 1] The paper contains two abstracts with contradictory quantitative claims. The top abstract states '27–70% reduction over the strongest baseline'; the Section 1 abstract states 'reduces long-horizon RMSE by 15–35%'. No table in the main text reports exact RMSE values; Figures 9 and 10 are bar charts without numeric labels or confidence intervals. This inconsistency and the absence of numerical tables prevent the reader from verifying the central empirical claim.
  3. [Sections 3–4, datasets] Section 4.3 lists four synthetic settings (SIRS Fixed, SIRS Varying, SIR, SEIRS) and two real datasets (ILI, CLS), i.e., six evaluation settings, while the abstract says 'all five datasets' and Figure 9's caption says 'real datasets' despite including synthetic results. The mapping from these settings to the claimed 'five datasets' is unclear, and the paper should state exactly which configurations constitute the five datasets.
  4. [Section 4.6.1] The parameter-recovery claims are qualitative. The text says the inferred β(t), γ(t), δ(t) and unobserved compartments 'closely follow' or 'closely track' ground truth, but no error metrics (e.g., RMSE, MAE, correlation) are reported for the synthetic experiments where ground-truth parameters and compartments are available. This weakens the paper's second main contribution and should be quantified.
  5. [Eq. (8)–(9); Algorithm 1] The residual component is denoted R(t) in Eq. (9) and Algorithm 1, but R(t) is also used for the recovered compartment in Eqs. (1) and (15). This naming collision is confusing in the description of the control path and should be resolved (e.g., use N(t) for residual as in Eq. (8)).
minor comments (6)
  1. [Throughout] The model name is written inconsistently as EpiNode and EpiNODE (e.g., 'EpiNODE' in Section 4.5.1, 'EpiNode' elsewhere). Please standardize.
  2. [Abstract, Section 1] Typo: 'relative strong time-series' should be 'relative to strong time-series'. Also 'Appdendix C' in Section 4.1 should be 'Appendix C'.
  3. [Eq. (13)] The notation '˜· ∈ (0,1)' is informal; the tilde symbol over the decoded parameters is not defined clearly. Please use explicit notation such as (β̃, γ̃, δ̃) ∈ (0,1)^3.
  4. [Figure 9] The caption says 'Overall benchmark RMSE on real datasets,' but the subplots (a)–(d) are synthetic SIRS/SIR/SEIRS and (e)–(f) are real. The caption should reflect that the figure includes all datasets.
  5. [Section 4, item 1(a)] The list says 'Section Appendix 4.5.2' for peak errors; this appears to be a formatting error and should be 'Section 4.5.2'.
  6. [Eq. (16)] The mass-correction coefficient α is overloaded with the VMD bandwidth penalty α in Eq. (4). Please use distinct symbols (e.g., α_m for the mass correction).

Circularity Check

1 steps flagged

EpiNode's 'long-horizon forecasts' are generated from full-series VMD controls that include the forecast window, reducing the headline RMSE/peak gains to in-sample reconstruction.

specific steps
  1. self definitional [Appendix B, Algorithm 1 (lines 1, 18–19, 25); Section 3, Eq. (17)]
    "Ensure: Forecasted states {ŷ(t_i)}_{i=0}^{T−1} ... 1: I(t) decomposition: {T_i, S_i, R_i}_{i=0}^{T−1} ← VMDDecompose({I_i}) (8) ... 18: if i < t_split then 19: Training loss: L ← L + w_i(Î(t_i)−I_i)^2 (17) ... 25: return {ŷ(t_i)}_{i=0}^{T−1} and {β(t_i), γ(t_i), δ(t_i)}_{i=0}^{T−1}"

    The VMD solved in Eqs. (3)–(7) is a global transform: the ADMM updates use Fourier transforms of the whole signal and enforce Σ_k u_k(t)=x(t). Algorithm 1 therefore builds the controls u^(T), u^(S), u^(R) for every i, including i ≥ t_split, directly from the infection values I_i that the model is supposed to predict. The training loss is restricted to i < t_split, but inference (lines 9–16, 25) runs the latent ODEs and SIRS rollout with test-window controls, so the forecast trajectory is a nonlinear function of the target trajectory's own TSR components. The reported 27–70% RMSE reductions and peak-accuracy gains thus reduce by construction to in-sample reconstruction, not causal forecasting. If VMD were applied only to the training segment, no extrapolation rule for the controls is given,

full rationale

The load-bearing derivation chain in the paper is: VMD decomposition of the infection series → TSR control signals → three latent Neural ODEs → fused parameter decoder → mechanistic SIRS rollout. Algorithm 1 performs the decomposition on the full sequence {I_i}_{i=0}^{T−1} before the split is used, and the constraint in Eq. (3) makes the modes reconstruct the signal exactly. Hence the controls at test times are deterministic functions of future observed infections, and the 'forecast' is conditioned on the target. Restricting the training loss to i < t_split (Eq. 17) does not make the procedure causal; it only means the network weights are not updated on the test portion. The claimed empirical superiority on long-horizon RMSE and peak metrics is therefore largely an in-sample fit. No self-citation or imported-uniqueness circularity was found; the failure-mode catalog, ablations, and parameter-recovery experiments are independent contributions. But the headline forecasting claim is compromised by construction, so the circularity score is high.

Axiom & Free-Parameter Ledger

7 free parameters · 6 axioms · 0 invented entities

The central claim rests on standard signal-processing assumptions (VMD exact reconstruction), SIRS as the true model class, an arbitrary initialization, a hand-set mass-correction coefficient, and—critically—an unstated method for continuing decomposition controls beyond the observation window. Several hyperparameters (VMD α, K, delay m/τ, latent dimensions, parameter ranges) are chosen by hand and not reported.

free parameters (7)
  • VMD bandwidth penalty α
    Controls mode bandwidth in Eq. (4); value not reported.
  • Number of VMD modes K = 3 (main)
    Decomposition order; ablation varies 1/2/3, but no per-dataset value is specified.
  • Delay embedding dimension m and lag τ
    Eq. (9); values not reported.
  • Mass-correction coefficient α (Eq. 16) = 0.9
    Hand-set in all experiments; projects SIRS state toward unit mass and changes the dynamics.
  • Latent dimensions d_T, d_S, d_R
    Architecture choice; not specified.
  • Disease-specific parameter ranges β, γ, δ
    Eq. (14); the min/max ranges for each disease are not given.
  • Loss weight schedule w_i = linear increase near boundary
    Eq. (17); the exact schedule is not specified.
axioms (6)
  • domain assumption SIRS model class correctly describes the epidemic
    Eq. (15) is the mechanistic core; robustness to SIR/SEIRS mismatch is tested only synthetically.
  • ad hoc to paper Initialization S(0)=1−I(0), R(0)=0
    Eq. (2) is arbitrary and not varied or justified.
  • ad hoc to paper Mass correction α=0.9 preserves enough physics
    Eq. (16) alters the SIRS trajectory and is not justified.
  • standard math VMD modes sum to x(t)
    Eq. (3) constraint; holds by construction of VMD.
  • ad hoc to paper Decomposition controls can be continued beyond t_split
    Algorithm 1 and Eqs. (8)–(11); load-bearing and unstated.
  • domain assumption Parameter ranges bound true rates
    Eqs. (13)–(14) assume rates lie in (0,1) after affine scaling.

pith-pipeline@v1.3.0-alltime-deepseek · 14572 in / 14732 out tokens · 142064 ms · 2026-08-03T03:55:50.144073+00:00 · methodology

0 comments
read the original abstract

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible, while neural components can capture non-stationary, data-adaptive effects. In practice, however, many seemingly straightforward couplings fail under partial observability and continually shifting transmission dynamics driven by behavior, waning immunity, seasonality, and interventions. We catalog these failure modes and show that robust performance requires making non-stationarity explicit: we extract and extrapolate multi-scale structure from the observed infection series and use it as an interpretable control signal for a controlled neural ODE coupled to an epidemiological model. Concretely, we decompose infections into trend, seasonal, and residual components and use these signals to drive continuous-time latent dynamics while jointly forecasting and inferring time-varying transmission, recovery, and immunity-loss rates. Across early outbreak and multi-wave regimes, our approach attains the lowest RMSE on all five datasets (27-70% reduction over the strongest baseline), achieves the best peak detection accuracy, and recovers time-varying epidemiological rates within ground-truth ranges, without relying on auxiliary covariates.

Figures

Figures reproduced from arXiv: 2602.06323 by Jiaming Cui, Naren Ramakrishnan, Ray Lee, Yiqi Su.

Figure 1
Figure 1. Figure 1: EpiNode accuracy as a function of lookback window and forecast horizon. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Failure of SIR forecasts from neural ODEs under full and partial observability at a train/forecast split of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Failure of SIR forecasts from AE-NODE under full and partial observability at a train/forecast split of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Failure of SIR forecasts from AE-NODE under short training windows, with bidirectional training. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Incorporating physics informed losses. (a) with only [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Failure of Neural CDE-ODE forecasts on real data under partial observability. Forecasts are good for SIRS [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Overview of the proposed EpiNode framework. The observed epidemic time series is decomposed into trend, seasonal, and residuals components, which serve as multi-scale control signals for latent Neural ODEs. The fused latent representation is decoded into time-varying epidemiological parameters and coupled with mechanistic SIRS dynamics to produce physically consistent forecasts and interpretable parameter … view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of forecasts on synthetic and real datasets. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Overall benchmark RMSE on real datasets. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Peak error (magnitude & timing) across datasets [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Unobserved compartments (a) and parameters (b) inferred from the full observation window. [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Inferred time-varying epidemiological parameters using the full observation window. (a) Estimated parameter [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Best (HHS 4) and worst (HHS 10) forecasts across HHS regions at split [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Ablation results across datasets. (a) Comparison of 1ODE vs. 3ODEs with and without time-delay [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] 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

37 extracted references · 10 canonical work pages

  1. [1]

    Anderson and Robert M

    Roy M. Anderson and Robert M. May.Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, 1992

    1992

  2. [2]

    On the accuracy of short-term COVID-19 fatality forecasts

    Nino Antulov-Fantulin and Lucas Böttcher. “On the accuracy of short-term COVID-19 fatality forecasts”. In: BMC Infectious Diseases22.1 (Mar. 2022), p. 251.DOI:10.1186/s12879-022-07205-9

    work page doi:10.1186/s12879-022-07205-9 2022

  3. [3]

    Forecasting sequential data using consistent Koopman autoencoders

    Omri Azencot et al. “Forecasting sequential data using consistent Koopman autoencoders”. In:Proceedings of the 37th International Conference on Machine Learning. ICML’20. JMLR.org, 2020

    2020

  4. [4]

    An empirical evaluation of generic convolutional and recurrent networks for sequence modeling

    Shaojie Bai, J. Zico Kolter, and Vladlen Koltun. “An empirical evaluation of generic convolutional and recurrent networks for sequence modeling”. In:arXiv preprint arXiv:1803.01271(2018)

    Pith/arXiv arXiv 2018

  5. [5]

    George E. P. Box, Gwilym M. Jenkins, and Gregory C. Reinsel.Time Series Analysis: Forecasting and Control. Wiley, 2015

    2015

  6. [6]

    Evaluating epidemic forecasts in an interval format

    Johannes Bracher et al. “Evaluating epidemic forecasts in an interval format”. In:PLoS Computational Biology 17.2 (2021), e1008618

    2021

  7. [7]

    A Predictive Model of the Start of Annual Influenza Epidemics

    Elisabet Castro Blanco et al. “A Predictive Model of the Start of Annual Influenza Epidemics”. In:Microorgan- isms12.7 (2024).ISSN: 2076-2607.DOI: 10.3390/microorganisms12071257.URL: https://www.mdpi. com/2076-2607/12/7/1257

    work page doi:10.3390/microorganisms12071257.url: 2024

  8. [8]

    Realistic distributions of infectious periods in epidemic models

    Simon Cauchemez and Neil M. Ferguson. “Realistic distributions of infectious periods in epidemic models”. In: Proceedings of the Royal Society B273.1596 (2006), pp. 2491–2499

    2006

  9. [9]

    Neural Ordinary Differential Equations

    Ricky T. Q. Chen et al. “Neural Ordinary Differential Equations”. In:Advances in Neural Information Processing Systems. Ed. by S. Bengio et al. V ol. 31. Curran Associates, Inc., 2018.URL:https://proceedings.neurips. cc/paper_files/paper/2018/file/69386f6bb1dfed68692a24c8686939b9-Paper.pdf

    2018

  10. [10]

    Neural ordinary differential equations

    Tian Qi Chen et al. “Neural ordinary differential equations”. In:NeurIPS(2018)

    2018

  11. [11]

    Inference of epidemic dynamics in the COVID-19 era and beyond

    Anne Cori and Adam Kucharski. “Inference of epidemic dynamics in the COVID-19 era and beyond”. In: Epidemics48 (2024), p. 100784.ISSN: 1755-4365.DOI: https://doi.org/10.1016/j.epidem.2024. 100784.URL:https://www.sciencedirect.com/science/article/pii/S1755436524000458

    work page doi:10.1016/j.epidem.2024 2024

  12. [12]

    Data needs for better surveillance and response to infectious disease threats

    Anne Cori, Britta Lassmann, and Pierre Nouvellet. “Data needs for better surveillance and response to infectious disease threats”. In:Epidemics43 (June 2023). Editorial, p. 100685.ISSN: 1755-4365.DOI: 10.1016/j.epidem. 2023.100685

    arXiv 2023

  13. [13]

    Variational Mode Decomposition

    Konstantin Dragomiretskiy and Dominique Zosso. “Variational Mode Decomposition”. In:IEEE Transactions on Signal Processing62.3 (2014), pp. 531–544.DOI:10.1109/TSP.2013.2288675

    arXiv 2014

  14. [14]

    Epidemiological Data Challenges: Planning for a More Robust Future Through Data Standards

    Geoffrey Fairchild et al. “Epidemiological Data Challenges: Planning for a More Robust Future Through Data Standards”. In:Frontiers in Public Health6 (2018), p. 336.DOI:10.3389/fpubh.2018.00336

    arXiv 2018

  15. [15]

    Short-term wind power forecasting based on SSA-VMD-LSTM

    Xiaozhi Gao et al. “Short-term wind power forecasting based on SSA-VMD-LSTM”. In:Energy Reports9 (2023). 2022 The 3rd International Conference on Power and Electrical Engineering, pp. 335–344.ISSN: 2352-4847. DOI: https://doi.org/10.1016/j.egyr.2023.05.181 .URL: https://www.sciencedirect.com/ science/article/pii/S2352484723009368

    work page doi:10.1016/j.egyr.2023.05.181 2023

  16. [16]

    The Mathematics of Infectious Diseases

    Herbert W. Hethcote. “The Mathematics of Infectious Diseases”. In:SIAM Review42.4 (2000), pp. 599–653

    2000

  17. [17]

    Long short-term memory

    Sepp Hochreiter and Jürgen Schmidhuber. “Long short-term memory”. In:Neural Computation9.8 (1997), pp. 1735–1780

    1997

  18. [18]

    TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting

    Songtao Huang et al. “TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting”. In:The Thirteenth International Conference on Learning Representations. 2025.URL: https://openreview.net/forum?id=wTLc79YNbh

    2025

  19. [19]

    Tracking the transmission dynamics of COVID-19 with a time-varying coefficient state-space model

    Joshua P. Keller et al. “Tracking the transmission dynamics of COVID-19 with a time-varying coefficient state-space model”. In:Statistics in Medicine41.15 (2022), pp. 2745–2767.DOI: https://doi.org/10. 1002/sim.9382 . eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.9382 .URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9382

    work page doi:10.1002/sim.9382 2022

  20. [20]

    Neural Controlled Differential Equations for Irregular Time Series

    Patrick Kidger et al. “Neural Controlled Differential Equations for Irregular Time Series”. In:Advances in Neural Information Processing Systems. Ed. by H. Larochelle et al. V ol. 33. Curran Associates, Inc., 2020, pp. 6696–6707.URL: https://proceedings.neurips.cc/paper_files/paper/2020/file/ 4a5876b450b45371f6cfe5047ac8cd45-Paper.pdf

    2020

  21. [21]

    KAN-ODEs: Kolmogorov–Arnold network ordinary differen- tial equations for learning dynamical systems and hidden physics

    Benjamin C. Koenig, Suyong Kim, and Sili Deng. “KAN-ODEs: Kolmogorov–Arnold network ordinary differen- tial equations for learning dynamical systems and hidden physics”. In:Computer Methods in Applied Mechanics and Engineering432 (2024), p. 117397.ISSN: 0045-7825.DOI: https://doi.org/10.1016/j.cma.2024. 117397.URL:https://www.sciencedirect.com/science/art...

    doi:10.1016/j.cma.2024 2024

  22. [22]

    Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting

    Shiyang Li, Xiaoyong Jin, Yao Xuan, et al. “Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting”. In:NeurIPS(2019)

    2019

  23. [23]

    Fully learnable deep wavelet transform for unsupervised monitoring of high-frequency time series

    Gabriel Michau, Gaetan Frusque, and Olga Fink. “Fully learnable deep wavelet transform for unsupervised monitoring of high-frequency time series”. In:Proceedings of the National Academy of Sciences119.8 (2022), e2106598119.DOI: 10.1073/pnas.2106598119 . eprint: https://www.pnas.org/doi/pdf/10.1073/ pnas.2106598119.URL:https://www.pnas.org/doi/abs/10.1073/...

    doi:10.1073/pnas.2106598119 2022

  24. [24]

    STL Decomposition of Time Series Can Benefit Forecasting Done by Statistical Methods but Not by Machine Learning Ones

    Zuokun Ouyang, Philippe Ravier, and Meryem Jabloun. “STL Decomposition of Time Series Can Benefit Forecasting Done by Statistical Methods but Not by Machine Learning Ones”. In:Engineering Proceedings 5.1 (2021).ISSN: 2673-4591.DOI: 10.3390/engproc2021005042 .URL: https://www.mdpi.com/2673- 4591/5/1/42

    work page doi:10.3390/engproc2021005042 2021

  25. [25]

    SPlots: A statistical tool to unfold data distributions

    M. Pivk and F.R. Le Diberder. “SPlots: A statistical tool to unfold data distributions”. In:Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 555.1 (2005), pp. 356–369.ISSN: 0168-9002.DOI: https://doi.org/10.1016/j.nima.2005.08.106 . URL:https://www.sciencedirect.com/science/arti...

    doi:10.1016/j.nima.2005.08.106 2005

  26. [26]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems

    Maziar Raissi, Paris Perdikaris, and George E. Karniadakis. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems”. In:Journal of Computational Physics378 (2019), pp. 686– 707

    2019

  27. [27]

    Gaussian Processes in Machine Learning

    Carl Edward Rasmussen. “Gaussian Processes in Machine Learning”. In:Advanced Lectures on Machine Learning: ML Summer Schools 2003, Canberra, Australia, February 2 - 14, 2003, Tübingen, Germany, August 4 - 16, 2003, Revised Lectures. Ed. by Olivier Bousquet, Ulrike von Luxburg, and Gunnar Rätsch. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004, pp. 63...

    work page doi:10.1007/978-3-540-28650- 2003

  28. [28]

    EINNs: epidemiologically-informed neural networks

    Alexander Rodríguez et al. “EINNs: epidemiologically-informed neural networks”. In:Proceedings of the Thirty-Seventh AAAI Conference on Artificial Intelligence and Thirty-Fifth Conference on Innovative Applica- tions of Artificial Intelligence and Thirteenth Symposium on Educational Advances in Artificial Intelligence. AAAI’23/IAAI’23/EAAI’23. AAAI Press,...

    work page doi:10.1609/aaai.v37i12 2023

  29. [29]

    Latent Ordinary Differential Equations for Irregularly-Sampled Time Series

    Yulia Rubanova, Ricky T. Q. Chen, and David K Duvenaud. “Latent Ordinary Differential Equations for Irregularly-Sampled Time Series”. In:Advances in Neural Information Processing Systems. Ed. by H. Wallach et al. V ol. 32. Curran Associates, Inc., 2019.URL: https://proceedings.neurips.cc/paper_files/ paper/2019/file/42a6845a557bef704ad8ac9cb4461d43-Paper.pdf

    2019

  30. [30]

    Epidemiology and Transmission Dynamics of Infectious Diseases and Control Measures

    Sukhyun Ryu et al. “Epidemiology and Transmission Dynamics of Infectious Diseases and Control Measures”. In:Viruses14.11 (Nov. 2022), p. 2510.DOI:10.3390/v14112510

    work page doi:10.3390/v14112510 2022

  31. [31]

    Forecasting seasonal outbreaks of influenza

    Jeffrey Shaman and Alicia Karspeck. “Forecasting seasonal outbreaks of influenza”. In:Proceedings of the National Academy of Sciences of the United States of America109.50 (Dec. 2012), pp. 20425–20430.ISSN: 0027-8424.DOI:10.1073/pnas.1208772109

    work page doi:10.1073/pnas.1208772109 2012

  32. [32]

    Physics-informed neural ODE (PINODE): embedding physics into models using collocation points

    Aleksei Sholokhov et al. “Physics-informed neural ODE (PINODE): embedding physics into models using collocation points”. In:Scientific Reports13.1 (2023), p. 10166.ISSN: 2045-2322.DOI: 10.1038/s41598-023- 36799-6.URL:https://doi.org/10.1038/s41598-023-36799-6

    doi:10.1038/s41598-023- 2023

  33. [33]

    Learning Koopman invariant subspaces for dynamic mode decomposition

    Naoya Takeishi, Yoshinobu Kawahara, and Takehisa Yairi. “Learning Koopman invariant subspaces for dynamic mode decomposition”. In:Proceedings of the 31st International Conference on Neural Information Process- ing Systems. NIPS’17. Long Beach, California, USA: Curran Associates Inc., 2017, pp. 1130–1140.ISBN: 9781510860964

    2017

  34. [34]

    EARTH: Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graph

    Guancheng Wan et al. “EARTH: Epidemiology-Aware Neural ODE with Continuous Disease Transmission Graph”. In:Forty-second International Conference on Machine Learning. 2025.URL: https://openreview. net/forum?id=Cnfogmxymj

    2025

  35. [35]

    TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis

    Shiyu Wang et al. “TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis”. In:The Thirteenth International Conference on Learning Representations. 2025.URL: https://openreview. net/forum?id=1CLzLXSFNn

    2025

  36. [36]

    Xiyuan Zhang et al.First De-Trend then Attend: Rethinking Attention for Time-Series Forecasting. 2022. arXiv: 2212.08151 [cs.LG].URL:https://arxiv.org/abs/2212.08151

    Pith/arXiv arXiv 2022

  37. [37]

    Informer: Beyond efficient transformer for long sequence time-series forecasting

    Haoyi Zhou et al. “Informer: Beyond efficient transformer for long sequence time-series forecasting”. In:AAAI (2021). 16 APREPRINT- FEBRUARY9, 2026 A Failure Modes We describe some of the architectures used for the experiments described in the Failure Modes section. Figure A1: Overview of bidirectional AE-NODE framework. Figure A2:Overview of Neural CDE-O...

    2021