Related papers: jInv -- a flexible Julia package for PDE parameter…
As the main theoretical support of quantum metrology, quantum parameter estimation must follow the steps of quantum metrology towards the applied science and industry. Hence, optimal scheme design will soon be a crucial and core task for…
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…
Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…
Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
Joint inversion refers to the simultaneous inference of multiple parameter fields from observations of systems governed by single or multiple forward models. In many cases these parameter fields reflect different attributes of a single…
Parameter estimation, which represents a classical inverse problem, is often ill-posed as different parameter combinations can yield identical outputs. This non-uniqueness poses a critical barrier to accurate and unique identification. This…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed…
Mathematical models of natural and man-made systems often have many adjustable parameters that must be estimated from multiple, potentially conflicting datasets. Rather than reporting a single best-fit parameter vector, it is often more…
This paper presents a high-performance framework for three-dimensional gravity modeling and inversion implemented in Julia, addressing key challenges in geophysical modeling such as computational complexity, ill-posedness, and the…
Modal methods for simulating vibrations of strings, membranes, and plates are widely used in acoustics and physically informed audio synthesis. However, traditional implementations, particularly for non-linear models like the von K\'arm\'an…
High fidelity models used in many science and engineering applications couple multiple physical states and parameters. Inverse problems arise when a model parameter cannot be determined directly, but rather is estimated using (typically…
In this paper we present BilevelJuMP, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the…
Large scale parameter estimation problems are among some of the most computationally demanding problems in numerical analysis. An academic researcher's domain-specific knowledge often precludes that of software design, which results in…
A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and to minimize total cost. We propose a probabilistic framework for multi-objective…
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of…
Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…