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Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…
By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…
Model predictive control (MPC) is a powerful technique for solving dynamic control tasks. In this paper, we show that there exists a close connection between MPC and online learning, an abstract theoretical framework for analyzing online…
A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…
Derived from the regular perturbation treatment of the nonlinear Schrodinger equation, a machine learning-based scheme to mitigate the intra-channel optical fiber nonlinearity is proposed. Referred to as the perturbation theory-aided (PA)…
Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. For example, this issue often limits the performance of model-based reinforcement learning and imitation…
For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to…
Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for sequential decision-making. However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value…
Designing motion control and planning algorithms for multilift systems remains challenging due to the complexities of dynamics, collision avoidance, actuator limits, and scalability. Existing methods that use optimization and distributed…
A propagator-based approach is investigated for Monte-Carlo (MC) modeling of neutral particles transport in fusion boundary plasmas. The propagator is essentially a Green function for the neutral kinetic equation, which depends on the…
Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a…
We present a Fourier transform methodology for all-order polarization mode dispersion (PMD) analysis, based on the first Born approximation to the coupled-mode equation solution. Our method predicts wavelength-dependent PMD effects and…
Simulating the dynamics of ions near polarizable nanoparticles (NPs) using coarse-grained models is extremely challenging due to the need to solve the Poisson equation at every simulation timestep. Recently, a molecular dynamics (MD) method…
In this work, we present a parallel scheme for machine learning of partial differential equations. The scheme is based on the decomposition of the training data corresponding to spatial subdomains, where an individual neural network is…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…