Related papers: Parsimony-Enhanced Sparse Bayesian Learning for Ro…
This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such…
The challenges for non-intrusive methods for Polynomial Chaos modeling lie in the computational efficiency and accuracy under a limited number of model simulations. These challenges can be addressed by enforcing sparsity in the series…
Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…
We propose a variational Bayesian (VB) implementation of block-sparse Bayesian learning (BSBL) to compute proxy probability density functions (PDFs) that approximate the posterior PDFs of the weights and associated hyperparameters in a…
The Broad Learning System (BLS) has gained significant attention for its computational efficiency and less network parameters compared to deep learning structures. However, the standard BLS relies on the pseudoinverse solution, which…
We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…
This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…
A modified Deep BSDE (backward differential equation) learning method with measurability loss, called Deep BSDE-ML method, is introduced in this paper to solve a kind of linear decoupled forward-backward stochastic differential equations…
Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…
We propose a sequential learning policy for noisy discrete global optimization and ranking and selection (R\&S) problems with high dimensional sparse belief functions, where there are hundreds or even thousands of features, but only a small…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Robust cognitive radio development requires accurate 3D path loss models. Traditional empirical models often lack environment-awareness, while deep learning approaches are frequently constrained by the scarcity of large-scale training…
This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that…