Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions
Pola Lydia Lagari, Lefteri H. Tsoukalas, Salar Safarkhani, I.E. Lagaris
Abstract
A systematic approach is developed for constructing proper trial solutions to Partial Differential Equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. The spatial domain considered is of the rectangular hyper-box type. On each face either Dirichlet or Neumann conditions may apply. Robin conditions may be accommodated as well. Interface conditions that induce discontinuities, have not been treated to date in the relevant neural network literature. As an illustration a common problem of heat conduction through a system of two rods in thermal contact is considered.
Topics & Concepts
Computer scienceInterface (matter)Classification of discontinuitiesPartial differential equationBoundary value problemBoundary (topology)Domain (mathematical analysis)Artificial neural networkNeumann boundary conditionThermal conductionDirichlet boundary conditionApplied mathematicsMathematical analysisMathematicsArtificial intelligencePhysicsMaximum bubble pressure methodThermodynamicsParallel computingBubbleModel Reduction and Neural NetworksNeural Networks and ApplicationsNumerical methods in engineering