A new entropy-compatible neural network method for scalar conservation laws is developed with explicit L1 convergence rates O(h^{1/2}) for shock-containing piecewise smooth entropy solutions.
arXiv preprint arXiv:2403.19234 (2024)
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Rothe's method stabilizes Gaussian wavepacket propagation for quantum dynamics, yielding grid-comparable accuracy for electronic and rovibrational processes including high-harmonic generation using remarkably few functions.
citing papers explorer
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A neural network method for scalar conservation laws with convergence rates for shock-wave solutions
A new entropy-compatible neural network method for scalar conservation laws is developed with explicit L1 convergence rates O(h^{1/2}) for shock-containing piecewise smooth entropy solutions.
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Rothe's Method for Quantum Dynamics in Atoms and Molecules with Gaussian Wavepackets
Rothe's method stabilizes Gaussian wavepacket propagation for quantum dynamics, yielding grid-comparable accuracy for electronic and rovibrational processes including high-harmonic generation using remarkably few functions.