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We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the…

Recently, a surrogate model was proposed that employs a factorization machine to approximate the underlying input-output mapping of the original system, with quantum annealing used to optimize the resulting surrogate function. Inspired by…

In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

Generative models such as diffusion models, excel at capturing high-dimensional distributions with diverse input modalities, e.g. robot trajectories, but are less effective at multi-step constraint reasoning. Task and Motion Planning (TAMP)…

Modeling groundwater flow in three-dimensional fractured crystalline media requires accounting for strong spatial heterogeneity induced by fractures. Fine-scale discrete fracture-matrix (DFM) simulations can capture this complexity but are…

The Dirichlet Process Gaussian Mixture Model (DPGMM) is often used to cluster data when the number of clusters is unknown. One main DPGMM inference paradigm relies on sampling. Here we consider a known state-of-art sampler (proposed by…

For economic nonlinear model predictive control and dynamic real-time optimization fast and accurate models are necessary. Consequently, the use of dynamic surrogate models to mimic complex rigorous models is increasingly coming into focus.…

There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational…

Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…

Large-scale international scientific collaborations, such as ATLAS, Belle II, CMS, and DUNE, generate vast volumes of data. These experiments necessitate substantial computational power for varied tasks, including structured data…

Machine learning surrogate emulators are needed in engineering design and optimization tasks to rapidly emulate computationally expensive physics-based models. In micromechanics problems the local full-field response variables are desired…

Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…

This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

Building local surrogates to accelerate stationary point searches on potential energy surfaces spans decades of effort. Done correctly, surrogates can reduce the number of expensive electronic structure evaluations by roughly an order of…