Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks

2024-02-02

Chaos, Solitons & Fractals

AI Summary

Jointly inferring the drift and diffusion terms of a Langevin equation from observed trajectories while quantifying predictive uncertainty remains a long-standing challenge. Method: This paper introduces Bayesian neural networks (BNNs) into the Langevin inversion framework for the first time, integrating physics-informed priors with variational inference to enable end-to-end, physically constrained, uncertainty-aware modeling. The approach ensures dynamical consistency via numerical stochastic differential equation (SDE) validation. Results: On both synthetic and real particle-tracking data, the method accurately recovers nonlinear drift and diffusion functions; its uncertainty estimates closely align with true errors, achieving a 42% improvement in calibration over conventional deterministic fitting methods—significantly advancing beyond their inherent limitations.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Problem

• Inferring Langevin equations from observed trajectories with uncertainty
• Assessing prediction uncertainties in stochastic systems via Bayesian networks
• Combining drift force and diffusion matrix for accurate Langevin modeling

Innovation

• Bayesian neural networks infer Langevin equations
• Separates drift force and diffusion matrix
• Provides prediction distributions for uncertainty assessment