Related papers: Correlational Lagrangian Schr\"odinger Bridge: Lea…
The dynamic Schr\"odinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Molecular Dynamics (MD) simulations provide a fundamental tool for characterizing molecular behavior at full atomic resolution, but their applicability is severely constrained by the computational cost. To address this, a surge of deep…
Cross-sectional studies are widely prevalent since they are more feasible to conduct compared to longitudinal studies. However, cross-sectional data lack the temporal information required to study the evolution of the underlying processes.…
Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in…
Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…
We consider the problem of sampling transition paths between two given metastable states of a molecular system, e.g. a folded and unfolded protein or products and reactants of a chemical reaction. Due to the existence of high energy…
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. In this paper, we build on previous work combining Schr\"odinger bridges and plug & play Langevin…
Computational methods for learning to sample from the Boltzmann distribution -- where the target distribution is known only up to an unnormalized energy function -- have advanced significantly recently. Due to the lack of explicit target…
Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization…
This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly…
Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…
This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying…
We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…
We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…
Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal…
Continual Learning (CL) poses a significant challenge in Artificial Intelligence, aiming to mirror the human ability to incrementally acquire knowledge and skills. While extensive research has focused on CL within the context of…
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians…
When governed by underlying low-dimensional dynamics, the interdependence of simultaneously recorded population of neurons can be explained by a small number of shared factors, or a low-dimensional trajectory. Recovering these latent…