Related papers: jInv -- a flexible Julia package for PDE parameter…
Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex…
Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient…
We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields (which are…
Evaluation of relativistic molecular integrals over exponential-type spinor orbitals require using the relativistic auxiliary functions in prolate spheroidal coordinates. They have derived recently by the author [Physical Review E 91,…
We introduce a method for efficiently solving initial-boundary value problems (IBVPs) that uses Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations,…
IntrinsicTimescales.jl is a Julia package to perform estimation of intrinsic neural timescales (INTs). INTs are defined as the time window in which prior information from an ongoing stimulus can affect the processing of newly arriving…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform…
We present a full implementation of the parareal algorithm---an integration technique to solve differential equations in parallel---in the Julia programming language for a fully general, first-order, initial-value problem. We provide a…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical…
Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…
Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…
In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…
We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…
Estimating parameters of Partial Differential Equations (PDEs) is of interest in a number of applications such as geophysical and medical imaging. Parameter estimation is commonly phrased as a PDE-constrained optimization problem that can…
Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…