Search papers, labs, and topics across Lattice.
This paper introduces a structure-aware, energy-based learning framework aimed at inferring unknown potential functions in generalized diffusion processes, addressing the challenges posed by noise and incomplete observations in classical methods. By leveraging the energetic variational approach and constructing loss functions from the De Giorgi dissipation functional, the authors ensure a robust coupling of free energy and dissipation without directly enforcing governing equations. Numerical experiments across multiple dimensions reveal that this approach significantly enhances robustness to noise and variability in training data, underscoring the utility of energy-dissipation principles in learning stochastic dynamics.
Energy-dissipation principles can revolutionize how we infer potential functions in noisy, incomplete data environments, achieving remarkable robustness in generalized diffusion processes.
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct regression of governing equations or velocity fields, which can be sensitive to noise and external perturbations and may fail when observations are incomplete. In this work, we propose a structure-aware, energy-based learning framework for inferring unknown potential functions in generalized diffusion processes, grounded in the energetic variational approach. Starting from the energy-dissipation law associated with the Fokker-Planck equation, we construct loss functions based on the De Giorgi dissipation functional, which consistently couple the free energy and the dissipation mechanism of the system. This formulation avoids explicit enforcement of the governing partial differential equation and preserves the underlying variational structure of the dynamics. Through numerical experiments in one, two, and three dimensions, we demonstrate that the proposed energy-based loss exhibits enhanced robustness with respect to observation time, noise level, and the diversity and amount of available training data. These results highlight the effectiveness of energy-dissipation principles as a reliable foundation for learning stochastic diffusion dynamics from data.
