arXiv Machine Learning
ZENO: Nonlinear filtering with Zakai Equation Neural Operators
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arXiv Machine Learning
Jul 22
Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise
arXiv:2607. 19173v1 Announce Type: new Abstract: Neural stochastic differential equations (SDEs) have emerged as powerful tools for learning noisy or stochastic dynamics directly from data; however, existing approaches largely assume uncoupled and continuous noise, limiting their applicability to realistic stochastic drivers, and often scale poorly in time, requiring expensive autoregressive training.
arXiv Machine Learning
Jul 1
A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements
arXiv:2606. 31137v1 Announce Type: new Abstract: This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements.
arXiv Machine Learning
Jun 9
Operator learning for solving Fokker-Planck equations with various initial conditions
arXiv:2606. 09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics.
arXiv Machine Learning
Jul 17
RTS Smoother-Guided Learning of Physics-Based Neural Differential Models
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
arXiv Machine Learning
Sep 30
Invertible continuous latent dynamic for long-term data assimilation in complex physical systems
arXiv:2602.02832v4 Announce Type: replace Abstract: Forward forecasting and data assimilation are the two important aspects in physical simulation: one propagates the state forward, the other recover...
arXiv AI
Aug 28
Physics-Informed Stochastic Configuration Machine: A Backpropagation-Free Neural Network with Fast Training for Nonlinear Differential Equations
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.