7 papers
Structure-Aware Variational Learning of a Class of Generalized Diffusions
Yubin Lu, Xiaofan Li, Chun Liu +2
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…
Learning Generalized Diffusions using an Energetic Variational Approach
Yubin Lu, Xiaofan Li, Chun Liu +2
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws a…
Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations
Yubin Lu, Chi-An Chen, Xiaofan Li +1
Keller-Segel systems are a set of nonlinear partial differential equations used to model chemotaxis in biology. In this paper, we propose two alternating direction implicit (ADI) s…
Entropy production rate and time-reversibility for general jump diffusions on
Qi Zhang, Yubin Lu
This paper investigates the entropy production rate and time-reversibility for general jump diffusions (Lévy processes) on . We first formulate the entropy productio…
Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts
Fanze Kong, Chen-Chih Lai, Yubin Lu
Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift…
Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
Fanze Kong, Chen-Chih Lai, Yubin Lu
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws wit…