φ-DeepONet learns mappings with discontinuities in inputs and outputs by combining multiple branch networks with a nonlinear interface embedding in the trunk, trained via physics- and interface-informed loss, and shows accurate results on 1D/2D benchmarks.
Physics-informed neural networks (pinns) for fluid mechanics: A review.Acta Mechanica Sinica, 37(12):1727–1738
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NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
AdamFLIP treats PDE constraint residuals in PINNs as a controlled dynamical system, computes Lagrange multipliers via feedback linearization to drive residuals to zero, and applies Adam-style adaptation to the resulting gradient for scalable hard-constrained training.
A language model-based operator learning method reconstructs flow fields from under 10% sparse measurements on vortex street, US temperature, blood flow, and turbulent jet benchmarks with competitive accuracy.
citing papers explorer
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$\phi-$DeepONet: A Discontinuity Capturing Neural Operator
φ-DeepONet learns mappings with discontinuities in inputs and outputs by combining multiple branch networks with a nonlinear interface embedding in the trunk, trained via physics- and interface-informed loss, and shows accurate results on 1D/2D benchmarks.
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Neural equilibria for long-term prediction of nonlinear conservation laws
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
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AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training
AdamFLIP treats PDE constraint residuals in PINNs as a controlled dynamical system, computes Lagrange multipliers via feedback linearization to drive residuals to zero, and applies Adam-style adaptation to the resulting gradient for scalable hard-constrained training.
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Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach
A language model-based operator learning method reconstructs flow fields from under 10% sparse measurements on vortex street, US temperature, blood flow, and turbulent jet benchmarks with competitive accuracy.