mlsanityData to 7 Oct 2026

Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots

arXiv 2607.01749 ↗First posted 2 Jul 2026q-bio.QM physics.bio-ph stat.MLcited by 0

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Abstract (arXiv)

Despite increasing scale and resolution, many biological measurements remain destructive, revealing only spatial information rather than the dynamics it encodes. By combining flexible representations with mechanistic constraints, physics-informed machine learning offers a promising route to inferring these dynamics from static snapshots. Motivated by subcellular imaging of gene expression, we ask when a static spatial pattern of molecules can identify spatially varying diffusivity, creation, destruction, and boundary exchange, and how different inference schemes perform on the task. A structural identifiability analysis shows that distributed sources are non-identifiable, whereas a point source such as a transcription site can restore identifiability. These limits are further shaped by seemingly innocuous modeling choices: the boundary conditions, the spatial regularity of the underlying dynamics, and even the stochastic calculus convention. We then adapt several physics-informed schemes, differing in how they represent the solution and enforce the governing equations, and demonstrate effective inference from a single snapshot. Physics-informed approaches can thus recover spatial heterogeneities of biological dynamics from static data, but their use should be accompanied and guided by careful identifiability analysis for meaningful interpretation of the results.

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References · 18

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  3. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  4. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  5. 2021Encoding physics to learn reaction-diffusion processescited by 61
  6. 2020Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networkscited by 52
  7. 2022Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networkscited by 23
  8. 2022A cusp-capturing PINN for elliptic interface problemscited by 16
  9. 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshotscited by 10
  10. 2024BiLO: Bilevel Local Operator Learning for PDE Inverse Problemscited by 8
  11. 2025Inferring stochastic dynamics with growth from cross-sectional datacited by 4
  12. 2025Position: Biology is the Challenge Physics-Informed ML Needs to Evolvecited by 4
6 more
  1. 2016Cox process representation and inference for stochastic reaction-diffusion processescited by 2
  2. 2025Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Methodcited by 2
  3. 2025Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptationcited by 2
  4. 2025Numerical PDE solvers outperform neural PDE solverscited by 2
  5. 2021Using neural networks to estimate parameters in spatial point process modelscited by 1
  6. 2026Physics-Informed Neural Networks for Biological 2D+t Reaction-Diffusion Systemscited by 1

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