Identifiability Limits of Physics-Informed Inference for Spatial Stochastic Dynamics from Static Snapshots
Rujie Gu, Ray Zirui Zhang, Christopher E. Miles
q-bio.QM, physics.bio-ph, stat.ML
Submitted: 2026-07-02
Comments: 29 pages, 9 figures
Code: https://github.com/Miles-group-code/AlphaDiffusivityNet
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
The gist: Despite increasing scale and resolution, many biological measurements remain destructive, revealing only spatial information rather than the dynamics it encodes.
Terminology
Abstract
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.
Sources
- Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems
- Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshots
- When do trajectories matter? Identifiability analysis for stochastic transport phenomena
- Numerical PDE solvers outperform neural PDE solvers
- Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method
- Escape from heterogeneous diffusion
- Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation
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