Affine transformations accelerate the training of physics-informed neural networks of a one-dimensional consolidation problem
Year: 2023
Type: article
Abstract: Physics-informed neural networks (PINNs) leverage data and knowledge about a problem. They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in PINNs for solving one-dimensional consolidation problems of porous media through the introduction of affine transformations after the classical output layer of artificial neural network architectures, effectively accelerating the training process. These affine physics-informed neural networks (AfPINNs) then produce nontrivial and accurate field solutions even in parameter spaces with diverging orders of magnitude. On average, AfPINNs show the ability to improve the [Formula: see text] relative error by [Formula: see text] after 25,000 epochs for a one-dimensional consolidation problem based on Biot's theory, and an average improvement by [Formula: see text] with a transfer approach to the theory of porous media.
Source: Scientific Reports
Institution: University of Stuttgart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,233
Awards: Methodenentwicklung zur robusten hybriden wissens und datengetriebene Modellordnungsreduktion für deformierbare poröse fluidgesättigte Materialien, G2022546044, G2514841155, CompLS - Runde 5 - Verbundprojekt: ATLAS - Al and Simulation for Tumor Liver Assessment - Entwicklung eines Systems zur klinischen Entscheidungsunterstützung in der Diagnose und Behandlung von Lebertumoren auf Basis von künstlicher Intelligenz und Simulationen - Teilprojekt A, G6129849046, Simulationsgestützte Bewertung von Spenderorganen vor Lebertransplantation (SimLivA) kontinuumsbiomechanische Modellierung für die Beurteilung von IschämieReperfusionsschäden, G7241049836, G7249683039, G7302806451, FOR 5151: Quantifizierung des Zusammenhanges zwischen Leberperfusion und funktion bei erweiterter Leberresektion Ein systemmedizinischer Ansatz (QuaLiPerF), EXC 2075: Datenintegrierte Simulationswissenschaft (SimTech)
OpenAlex ID: W4386890307