Related papers: jInv -- a flexible Julia package for PDE parameter…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equations (PDEs) in strong form. We employ both Isogeometric…
Many uncertainty propagation software exist, written in different programming languages, but not all of them are able to handle functional correlation between quantities. In this paper we review one strategy to deal with uncertainty…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but…
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
We present the SLIM (https://github.com/slimgroup) open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment…
Structural seismic interpretation and quantitative characterization are historically intertwined processes. The latter provides estimates of properties of the subsurface which can be used to aid structural interpretation alongside the…
Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to…
Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…
Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petro-elastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The…
Neural rendering has advanced significantly in 3D reconstruction and novel view synthesis, and integrating physics into these frameworks opens new applications such as physically accurate digital twins for robotics and XR. However, the…
Physics-informed Machine Learning has recently become attractive for learning physical parameters and features from simulation and observation data. However, most existing methods do not ensure that the physics, such as balance laws (e.g.,…
We present a method for computing the inverse parameters and the solution field to inverse parametric PDEs based on randomized neural networks. This extends the local extreme learning machine technique originally developed for forward PDEs…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
We present NEP-PACK a novel open-source library for the solution of nonlinear eigenvalue problems (NEPs). The package provides a framework to represent NEPs, as well as efficient implementations of many state-of-the-art algorithms. The…
This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimised software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the…