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We develop a new computational framework to solve sequential Bayesian optimal experimental design (SBOED) problems constrained by large-scale partial differential equations with infinite-dimensional random parameters. We propose an adaptive…

Computational Engineering, Finance, and Science · Computer Science 2024-10-04 Jinwoo Go , Peng Chen

The Monte Carlo-type Neural Operator (MCNO) introduces a lightweight architecture for learning solution operators for parametric PDEs by directly approximating the kernel integral using a Monte Carlo approach. Unlike Fourier Neural…

Machine Learning · Computer Science 2025-11-25 Salah Eddine Choutri , Prajwal Chauhan , Othmane Mazhar , Saif Eddin Jabari

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Giacomo Bottacini , Matteo Torzoni , Andrea Manzoni

Bayesian inference methods such as Markov Chain Monte Carlo (MCMC) typically require repeated computations of the likelihood function, but in some scenarios this is infeasible and alternative methods are needed. Simulation-based inference…

Machine Learning · Computer Science 2025-12-10 Linnea M Wolniewicz , Peter Sadowski , Claudio Corti

Continuum robots enable dexterous manipulation in constrained environments, but require accurate and efficient models for real-time manipulation and control. Traditional physics-based models can be computationally expensive and may suffer…

Robotics · Computer Science 2026-05-20 Branden Frieden , James M. Ferguson , Alan Kuntz , Varun Shankar

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…

Computational Physics · Physics 2026-01-16 Jeongjin Park , Grant Bruer , Huseyin Tuna Erdinc , Abhinav Prakash Gahlot , Felix J. Herrmann

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

Machine Learning · Computer Science 2025-06-03 Jin Song , Kenji Kawaguchi , Zhenya Yan

Driven by advances in hardware and software technologies, nonlinear model predictive control (NMPC) has gained increasing adoption in both industry and academia over the past decades. However, its practical deployment is often limited by…

Optimization and Control · Mathematics 2026-04-10 Perceval Beja-Battais , Guillaume Dupré , Alain Grossetête , Nicolas Vayatis

Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses…

Numerical Analysis · Mathematics 2025-06-17 Chenyu Zeng , Yanshu Zhang , Jiayi Zhou , Yuhan Wang , Zilin Wang , Yuhao Liu , Lei Wu , Daniel Zhengyu Huang

Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…

Numerical Analysis · Mathematics 2024-11-28 Paolo Villani , Daniel Andrés-Arcones , Jörg F. Unger , Martin Weiser

We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such…

Numerical Analysis · Mathematics 2021-02-09 Harbir Antil , Howard C Elman , Akwum Onwunta , Deepanshu Verma

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial…

Numerical Analysis · Mathematics 2023-05-03 Lianghao Cao , Thomas O'Leary-Roseberry , Prashant K. Jha , J. Tinsley Oden , Omar Ghattas

In multi-body dynamics, the motion of a complicated physical object is described as a coupled ordinary differential equation system with multiple unknown solutions. Engineers need to constantly adjust the object to meet requirements at the…

Computational Engineering, Finance, and Science · Computer Science 2022-05-26 Wenhao Ding , Qing He , Hanghang Tong , Ping Wang

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…

Computation · Statistics 2016-05-03 Tiangang Cui , Kody J. H. Law , Youssef M. Marzouk

We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the…

Numerical Analysis · Mathematics 2013-05-01 Viet Ha Hoang , Christoph Schwab , Andrew M. Stuart

Computationally efficient surrogates for parametrized physical models play a crucial role in science and engineering. Operator learning provides data-driven surrogates that map between function spaces. However, instead of full-field…

Machine Learning · Computer Science 2024-12-31 Daniel Zhengyu Huang , Nicholas H. Nelsen , Margaret Trautner

MCMC methods for sampling from the space of DAGs can mix poorly due to the local nature of the proposals that are commonly used. It has been shown that sampling from the space of node orders yields better results [FK03, EW06]. Recently,…

Machine Learning · Computer Science 2012-06-26 Daniel Eaton , Kevin Murphy

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Computation · Statistics 2024-08-06 Chenyang Zhong , Shouxuan Ji , Tian Zheng

This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…

Machine Learning · Computer Science 2024-08-05 Bo Xu , Xinliang Liu , Lei Zhang

High-Performance Computing (HPC) schedulers must balance user performance with facility-wide resource constraints. The task boils down to selecting the optimal number of nodes for a given job. We present a surrogate-assisted multi-objective…

Machine Learning · Computer Science 2026-01-23 Ashna Nawar Ahmed , Banooqa Banday , Terry Jones , Tanzima Z. Islam