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Combining model-based and model-free deep reinforcement learning has shown great promise for improving sample efficiency on complex control tasks while still retaining high performance. Incorporating imagination is a recent effort in this…
It is well known that the diffusion equation, when treated as a stand-alone partial differential equation, exhibits exponential instabilities in boosted frames, which render the corresponding initial-value problem ill-posed. Recently,…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
Domain generalization refers to the problem where we aim to train a model on data from a set of source domains so that the model can generalize to unseen target domains. Naively training a model on the aggregate set of data (pooled from all…
We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate…
We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed away from the $x$-axis. We first analyze the case where the…
The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the…
Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent…
Finding the optimal design of experiments in the Bayesian setting typically requires estimation and optimization of the expected information gain functional. This functional consists of one outer and one inner integral, separated by the…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
A fluid flow in a multiply connected domain generated by an arbitrary number of point vortices is considered. A stream function for this flow is constructed as a limit of a certain functional sequence using the method of images. The…
Spatial sound field interpolation relies on suitable models to both conform to available measurements and predict the sound field in the domain of interest. A suitable model can be difficult to determine when the spatial domain of interest…
Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…
We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test…
For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from…
The estimation of physical parameters from data analysis is a crucial point for the description and modeling of many complex systems. Based on R\'enyi $\alpha$-Gaussian distribution and patched Green's function (PGF) techniques, we propose…
We propose a reduced basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we start by applying said transform to the evolution problem, yielding a…
Model-Based Reinforcement Learning involves learning a \textit{dynamics model} from data, and then using this model to optimise behaviour, most often with an online \textit{planner}. Much of the recent research along these lines presents a…
Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field…
We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…