Learning Coupled System Dynamics under Incomplete Physical Constraints and Missing Data
Advances in data acquisition and computational methods have accelerated the use of differential equation based modelling for complex systems. Such systems are often described by coupled (or more) variables, yet governing equation is typically available for one variable, while the remaining variable can be accessed only through data. This mismatch between known physics and observed data poses a fundamental challenge for existing physics-informed machine learning approaches, which generally assume either complete knowledge of the governing equations or full data availability across all variables. In this paper, we introduce MUSIC (Multitask Learning Under Sparse and Incomplete Constraints), a sparsity induced multitask neural network framework that integrates partial physical constraints with data-driven learning to recover full-dimensional solutions of coupled systems when physics-constrained and data-informed variables are mutually exclusive. MUSIC employs mesh-free (random) sampling of training data and sparsity regularization, yielding highly compressed models with improved training and evaluation efficiency. We demonstrate that MUSIC accurately learns solutions (shock wave solutions, discontinuous solutions, pattern formation solutions) to complex coupled systems under data-scarce and noisy conditions, consistently outperforming non-sparse formulations. These results highlight MUSIC as a flexible and effective approach for modeling partially observed systems with incomplete physical knowledge.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Incomplete Data, Complete Dynamics: A Diffusion Approach
Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges …
An incomplete equilibrium with a stochastic annuity
We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimize their expected utility over both running consumption and terminal wealth. The market co…
Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator
Analog quantum simulators provide access to many-body dynamics beyond the reach of classical computation. However, extracting physical insights from experimental data is often hindered by measurement noise, limited obser…
Dynamic Reservoir Computing with Physical Neuromorphic Networks
Reservoir Computing (RC) with physical systems requires an understanding of the underlying structure and internal dynamics of the specific physical reservoir. In this study, physical nano-electronic networks with neuromo…
Time Series PredictionPhysics-Informed Neural Learning for State Reconstruction and Parameter Identification in Coupled Greenhouse Climate Dynamics
Physics-informed neural networks (PINNs) have recently emerged as a promising framework for integrating data-driven learning with physical knowledge. In this work, we propose a coupled PINN approach for the joint reconst…