Related papers: jInv -- a flexible Julia package for PDE parameter…
Bayesian inference has become an important tool to solve inverse problems and to quantify uncertainties in their solutions. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently by using optimization.…
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
Inverse problems occur in a variety of parameter identification tasks in engineering. Such problems are challenging in practice, as they require repeated evaluation of computationally expensive forward models. We introduce a unifying…
We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations. Gridap is an open-source software project exclusively written in the Julia…
This paper discusses the algorithms and implementations of three Mathematica packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial PDEs. The first package, PainleveTest.m, symbolically…
We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus…
Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving…
Context. Inferring spectral parameters from X-ray data is one of the cornerstones of high-energy astrophysics, and is achieved using software stacks that have been developed over the last twenty years and more. However, as models get more…
Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics. A central challenge in using PDEs for real-world applications is…
InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging…
Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical…
We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the problem of optimal observation sensor placement for Bayesian…
In this paper, we develop a class of interacting particle Langevin algorithms to solve inverse problems for partial differential equations (PDEs). In particular, we leverage the statistical finite elements (statFEM) formulation to obtain a…
Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix…
We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an…
We introduce $\texttt{RandomMeas$.$jl}$, a modular and high-performance open-source software package written in Julia for implementing and analyzing randomized measurement protocols in quantum computing. Randomized measurements provide a…
Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…
Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…