32 citations · 125 across the 15 of their papers we have counts for
16 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…
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…
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 production…
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…
Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
Cheng Fang, Yubin Lu, Ting Gao +1
The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir…
Multi-task Meta Label Correction for Time Series Prediction
Luxuan Yang, Ting Gao, Wei Wei +3
Time series classification faces two unavoidable problems. One is partial feature information and the other is poor label quality, which may affect model performance. To address th…
Mathematical analysis of singularities in the diffusion model under the submanifold assumption
Yubin Lu, Zhongjian Wang, Guillaume Bal
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectatio…
An end-to-end deep learning approach for extracting stochastic dynamical systems with -stable Lévy noise
Cheng Fang, Yubin Lu, Ting Gao +1
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of…
Neural network stochastic differential equation models with applications to financial data forecasting
Luxuan Yang, Ting Gao, Yubin Lu +2
In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic t…
Extracting stochastic dynamical systems with -stable Lévy noise from data
Yang Li, Yubin Lu, Shengyuan Xu +1
With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the…
Extracting Stochastic Governing Laws by Nonlocal Kramers-Moyal Formulas
Yubin Lu, Yang Li, Jinqiao Duan
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems fro…
Learning the temporal evolution of multivariate densities via normalizing flows
Yubin Lu, Romit Maulik, Ting Gao +3
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporall…
Detecting the maximum likelihood transition path from data of stochastic dynamic systems
Min Dai, Ting Gao, Yubin Lu +2
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data…
Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise
Yubin Lu, Jinqiao Duan
It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the inv…