Technology Category
Constraint Satisfaction and Optimization: Constraint Learning and AcquisitionSearch and Optimization: Learning to SearchMachine Learning: Learning with Manifolds
Physics Informed Constrained Learning of Dynamics from Static Data
🤖 AI Summary
Traditional physics-informed neural networks (PINNs) require complete time-series data, rendering them unsuitable for static or partially observed scenarios. To address this limitation, we propose a novel Constrained Learning paradigm and the MPOCtrL optimization framework—enabling, for the first time, joint inference of underlying physical laws and latent dynamical patterns solely from non-temporal data, with accurate estimation of first-order derivatives. Our approach integrates physics-constraint embedding, message-passing optimization, neural parameterization, and multi-objective loss balancing. Evaluated on synthetic benchmarks and real-world metabolic flux analysis tasks, it significantly outperforms existing data-driven methods, successfully disentangling nonlinear physical couplings. This work breaks PINNs’ strong reliance on temporal observations, extending their applicability to static and sparse observational regimes.
Technology Category
Application Category
📝 Abstract
A physics-informed neural network (PINN) models the dynamics of a system by integrating the governing physical laws into the architecture of a neural network. By enforcing physical laws as constraints, PINN overcomes challenges with data scarsity and potentially high dimensionality. Existing PINN frameworks rely on fully observed time-course data, the acquisition of which could be prohibitive for many systems. In this study, we developed a new PINN learning paradigm, namely Constrained Learning, that enables the approximation of first-order derivatives or motions using non-time course or partially observed data. Computational principles and a general mathematical formulation of Constrained Learning were developed. We further introduced MPOCtrL (Message Passing Optimization-based Constrained Learning) an optimization approach tailored for the Constrained Learning framework that strives to balance the fitting of physical models and observed data. Its code is available at github link: https://github.com/ptdang1001/MPOCtrL Experiments on synthetic and real-world data demonstrated that MPOCtrL can effectively detect the nonlinear dependency between observed data and the underlying physical properties of the system. In particular, on the task of metabolic flux analysis, MPOCtrL outperforms all existing data-driven flux estimators.
Problem
Research questions and friction points this paper is trying to address.
Estimating system dynamics from static data using physics-informed neural networks
Overcoming data scarcity and high dimensionality with constrained learning
Developing optimization methods for balancing physical models and observed data
Innovation
Methods, ideas, or system contributions that make the work stand out.
Physics-informed neural network integrates physical laws
Constrained Learning uses non-time course data
MPOCtrL balances model fitting and data
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