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We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for…
It is common and convenient to treat distributed physical parameters as Gaussian random fields and model them in an "inverse procedure" using measurements of various properties of the fields. This article presents a general method for this…
Bayesian observer and actor models have provided normative explanations for many behavioral phenomena in perception, sensorimotor control, and other areas of cognitive science and neuroscience. They attribute behavioral variability and…
Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat\'ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based…
Solving Bayesian inverse problems typically involves deriving a posterior distribution using Bayes' rule, followed by sampling from this posterior for analysis. Sampling methods, such as general-purpose Markov chain Monte Carlo (MCMC), are…
In this paper, we study simultaneous determination of the strain hardening exponent, the shear modulus and the yield stress in an inverse problem. First, we analyze the direct and the inverse problems. Then we formulate the inverse problem…
Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of…
We review our recent work in the area of autonomous materials research, highlighting the coupling of machine learning methods and models and more problem-aware modeling. We review the general Bayesian framework for closed-loop design…
Robots need to estimate the material and dynamic properties of objects from observations in order to simulate them accurately. We present a Bayesian optimization approach to identifying the material property parameters of objects based on a…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…
Parameter estimation is a major challenge in computational modeling of biological processes. This is especially the case in image-based modeling where the inherently quantitative output of the model is measured against image data, which is…
A key task in the emerging field of materials informatics is to use machine learning to predict a material's properties and functions. A fast and accurate predictive model allows researchers to more efficiently identify or construct a…
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
In many applications involving point pattern data, the Poisson process assumption is unrealistic, with the data exhibiting a more regular spread. Such a repulsion between events is exhibited by trees for example, because of competition for…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…
A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…
We present Intrinsic Image Diffusion, a generative model for appearance decomposition of indoor scenes. Given a single input view, we sample multiple possible material explanations represented as albedo, roughness, and metallic maps.…
We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observation is often hard to…