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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Projected Inverse Iteration reframes ground-state search for neural quantum states as an eigenvalue problem to deliver rapid, spectral-gap-insensitive convergence while retaining polynomial scaling.
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.
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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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Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
Projected Inverse Iteration reframes ground-state search for neural quantum states as an eigenvalue problem to deliver rapid, spectral-gap-insensitive convergence while retaining polynomial scaling.
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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.