Related papers: Comprehensive Framework for Controlling Nonlinear …
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…
In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely used in multi-objective optimization and has recently found important applications in multi-criteria anomaly detection. Recently, a partial differential equation (PDE)…
Multispecies contaminant transport in the Earth's subsurface is commonly modelled using advection-dispersion equations coupled via first-order reactions. Analytical and semi-analytical solutions for such problems are highly sought after but…
Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…
The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
State estimation (SE) of water distribution networks (WDNs) is difficult to solve due to nonlinearity/nonconvexity of water flow models, uncertainties from parameters and demands, lack of redundancy of measurements, and inaccurate flow and…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Water scarcity and the low quality of wastewater produced in industrial applications present significant challenges, particularly in managing fresh water intake and reusing residual quantities. These issues affect various industries,…
The use of in-situ digital sensors for water quality monitoring is becoming increasingly common worldwide. While these sensors provide near real-time data for science, the data are prone to technical anomalies that can undermine the…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
Fluid models are a popular formalism in the quantitative modeling of biochemical systems and analytical performance models. The main idea is to approximate a large-scale Markov chain by a compact set of ordinary differential equations…
Multimodal optimization requires finding many optima rather than merely keeping a diverse population. Yet most niching-based evolutionary algorithms rely on distances or density estimators without explicitly recovering the underlying…