Hypothesis-driven construction of mesoscopic dynamics

• URL: http://arxiv.org/abs/2605.16211v1
• Date: Fri, 15 May 2026 17:26:28 GMT
• Title: Hypothesis-driven construction of mesoscopic dynamics
• Abstract summary: We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class.<n>We introduce a unified framework encompassing both dissipative and conservative meoscopic dynamics.<n>Data from each problem instance is then used to guide the identification of members within our hypothesis class.
• Score: 29.742281675145232
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including global well-posedness, asymptotic stability, unique factorization identifiability, and discrete energy dissipation, applicable to all spatio-temporal evolution equations within this hypothesis class prior to all learning stages. Data from each problem instance is then used to guide the identification of members within our hypothesis class, giving rise to accurate, robust and interpretable dynamical models. We empirically validate this framework on both data from continuum PDE models as a check, and on data arising from microscopic chain models for which exact meso-scale models are unknown. The proposed approach not only acts as an effective dynamics learner, but also offers vital interpretable diagnostics of the underlying physics.

Related papers

• CDFM: Towards a General-Purpose Causal Discovery Foundation Model [62.32138962508216]
  Causal discovery is the process of recovering underlying causal structures from observational data.<n>We formulate the Causal Discovery Foundation Model (CDFM) as a unified, general-purpose framework for zero-shot structural inference.<n>CDFM consistently outperforms traditional algorithms, driving a paradigm shift toward a general-purpose causal discovery foundation model.
  arXiv  Detail & Related papers  (2026-07-13T12:58:28Z)
• The Interplay of Data Structure and Imbalance in the Learning Dynamics of Diffusion Models [8.547042933482645]
  We study class-dependent learning in score-based diffusion models.<n>We reveal the explicit hierarchy governing these dynamics.<n>We validate our theoretical predictions empirically using U-Net models trained on Fashion MNIST.
  arXiv  Detail & Related papers  (2026-05-07T14:44:53Z)
• Universal Learning of Stochastic Dynamics for Exact Belief Propagation using Bernstein Normalizing Flows [10.143540866021542]
  This paper establishes the theoretical foundations for a class of models that satisfy both properties.<n>The proposed approach combines the expressiveness of normalizing density estimation with the analytical tractability of Bernsteins flows.
  arXiv  Detail & Related papers  (2025-09-19T02:36:35Z)
• No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs [56.78271181959529]
  This paper proposes a conceptual shift to modeling low-dimensional dynamical systems by departing from the traditional two-step modeling process.<n>Instead of first discovering a closed-form equation and then analyzing it, our approach, direct semantic modeling, predicts the semantic representation of the dynamical system.<n>Our approach not only simplifies the modeling pipeline but also enhances the transparency and flexibility of the resulting models.
  arXiv  Detail & Related papers  (2025-01-30T18:36:48Z)
• Finding the Underlying Viscoelastic Constitutive Equation via Universal Differential Equations and Differentiable Physics [1.03121181235382]
  This research employs Universal Differential Equations (UDEs) alongside differentiable physics to viscoelastic fluids.<n>This study focuses on analyzing four viscoelastic models: Upper Convected Maxwell (UCM), Johnson-Segalman, Giesekus, and Exponential Phan-Thien-Tanner (ePTT)
  arXiv  Detail & Related papers  (2024-12-31T17:34:29Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Generalized Neural Closure Models with Interpretability [28.269731698116257]
  We develop a novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models.
  arXiv  Detail & Related papers  (2023-01-15T21:57:43Z)
• Evolution TANN and the discovery of the internal variables and evolution equations in solid mechanics [0.0]
  We propose a new approach which allows, for the first time, to decouple the material representation from the incremental formulation. Inspired by the Thermodynamics-based Artificial Neural Networks (TANN) and the theory of the internal variables, the evolution TANN (eTANN) are continuous-time. Key feature of the proposed approach is the discovery of the evolution equations of the internal variables in the form of ordinary differential equations.
  arXiv  Detail & Related papers  (2022-09-27T09:25:55Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)

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.