Discrete Math. Algorithms Appl

We propose a conservative physics-informed neural network cPINN on discrete domains for nonlinear conservation laws. SIAM Journal on Optimization 9 4 965-990.


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Discrete math. algorithms appl. Here the term discrete domain represents the discrete sub-domains obtained after division of the computational domain where PINN is applied and the conservation property of cPINN is obtained by enforcing the flux continuity in the strong form. We have analyzed the statistical properties of solutions to the Burgers equation with random initial data and random forcing. For a circle of radius r the circumference and area are given by C 2pir 1 A pir2.

2 Similarly for a sphere of radius r the surface area and volume. There are many formulas of pi of many types. This series of work provided answers to some of the questions that Burgers proposed back in the early 20th century and resolved some of controversies concerning the asymptotics of the probability distribution functions for the random forced.

Among others these include series products geometric constructions limits special values and pi iterations. Pi is intimately related to the properties of circles and spheres. 1999 A Global Convergence Theory for Dennis El-Alem and Maciels Class of Trust-Region Algorithms for Constrained Optimization without Assuming Regularity.

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