Evaluating PDE discovery methods for multiscale modeling of biological signals

• URL: http://arxiv.org/abs/2506.20694v1
• Date: Wed, 25 Jun 2025 08:43:37 GMT
• Title: Evaluating PDE discovery methods for multiscale modeling of biological signals
• Authors: Andréa Ducos, Audrey Denizot, Thomas Guyet, Hugues Berry,
• Abstract summary: Biological systems are non-linear, including unobserved variables and the physical principles that govern their dynamics are partly unknown.<n>To address the challenge of bridging gaps between scales, we leverage partial differential equations (PDE) discovery.<n>PDE discovery suggests meso-scale dynamics characteristics from micro-scale data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Biological systems are non-linear, include unobserved variables and the physical principles that govern their dynamics are partly unknown. This makes the characterization of their behavior very challenging. Notably, their activity occurs on multiple interdependent spatial and temporal scales that require linking mechanisms across scales. To address the challenge of bridging gaps between scales, we leverage partial differential equations (PDE) discovery. PDE discovery suggests meso-scale dynamics characteristics from micro-scale data. In this article, we present our framework combining particle-based simulations and PDE discovery and conduct preliminary experiments to assess equation discovery in controlled settings. We evaluate five state-of-the-art PDE discovery methods on particle-based simulations of calcium diffusion in astrocytes. The performances of the methods are evaluated on both the form of the discovered equation and the forecasted temporal variations of calcium concentration. Our results show that several methods accurately recover the diffusion term, highlighting the potential of PDE discovery for capturing macroscopic dynamics in biological systems from microscopic data.

Related papers

• Principled model selection for stochastic dynamics [0.0]
  PASTIS is a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters.<n>It reliably identifies minimal models, even with low sampling rates or measurement error.<n>It applies to partial differential equations, and applies to ecological networks and reaction-diffusion dynamics.
  arXiv  Detail & Related papers  (2025-01-17T18:23:16Z)
• Ensemble WSINDy for Data Driven Discovery of Governing Equations from Laser-based Full-field Measurements [0.0]
  This work leverages laser vibrometry and the weak form of the weak identification of nonlinear dynamics (WSINDy) for partial differential equations. Two beam-like specimens, one aluminum and one IDOX/Estane composite, are subjected to wave shear excitation in the low frequency regime. The WSINDy for PDEs algorithm is applied to the resulting-temporal data to discover the effective dynamics of the specimens.
  arXiv  Detail & Related papers  (2024-09-30T17:12:19Z)
• Stochastic Schr\"odinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective [3.105656247358225]
  We develop a framework to simulate dynamics of Anderson-Holstein impurities coupled to a continuous fermionic bath. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and master equations.
  arXiv  Detail & Related papers  (2023-09-16T06:03:54Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers.<n>We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.<n>Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data [0.6882042556551611]
  We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs) The fine scale, detailed, hybrid (continuum - Monte Carlo) simulation model embodies the underlying biophysics. We learn effective, coarse-grained "Keller-Segel class" chemotactic PDEs using machine learning regressors.
  arXiv  Detail & Related papers  (2022-05-26T03:02:49Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Provable RL with Exogenous Distractors via Multistep Inverse Dynamics [85.52408288789164]
  Real-world applications of reinforcement learning (RL) require the agent to deal with high-dimensional observations such as those generated from a megapixel camera. Prior work has addressed such problems with representation learning, through which the agent can provably extract endogenous, latent state information from raw observations. However, such approaches can fail in the presence of temporally correlated noise in the observations.
  arXiv  Detail & Related papers  (2021-10-17T15:21:27Z)
• Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression [71.7560927415706]
  latent hybridisation model (LHM) integrates a system of expert-designed ODEs with machine-learned Neural ODEs to fully describe the dynamics of the system. We evaluate LHM on synthetic data as well as real-world intensive care data of COVID-19 patients.
  arXiv  Detail & Related papers  (2021-06-05T11:42:45Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• Inference of Stochastic Dynamical Systems from Cross-Sectional Population Data [8.905677748354364]
  Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on differential equations. Then, following the USDL approach, we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations.
  arXiv  Detail & Related papers  (2020-12-09T14:02:29Z)
• Particles to Partial Differential Equations Parsimoniously [0.0]
  coarse-grained effective Partial Differential Equations can lead to considerable savings in computation-intensive tasks like prediction or control. We propose a framework combining artificial neural networks with multiscale computation, in the form of equation-free numerics. We illustrate our approach by extracting coarse-grained evolution equations from particle-based simulations with a priori unknown macro-scale variable.
  arXiv  Detail & Related papers  (2020-11-09T15:51:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.