Related papers: Path-OED for infinite-dimensional Bayesian linear …
Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…
Automated chemical synthesis, materials fabrication, and spectroscopic physical measurements often bring forth the challenge of process trajectory optimization, i.e., discovering the time dependence of temperature, electric field, or…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
We propose a novel holistic approach for safe autonomous exploration and map building based on constrained Bayesian optimisation. This method finds optimal continuous paths instead of discrete sensing locations that inherently satisfy…
We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…
This paper deals with the gradient extremum seeking control for static scalar maps with actuators governed by distributed diffusion partial differential equations (PDEs). To achieve the real-time optimization objective, we design a…
Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems…
Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
This paper provides a detailed theoretical analysis of methods to approximate the solutions of high-dimensional (>10^6) linear Bayesian problems. An optimal low-rank projection that maximizes the information content of the Bayesian…
Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations, or experiments which…
Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters.…
Bayesian optimal experimental design (BOED) is a methodology to identify experiments that are expected to yield informative data. Recent work in cognitive science considered BOED for computational models of human behavior with tractable and…
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…
Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a…
In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data must be informative about the unknown parameters. How to…