For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption
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A universal shallow water equations solver integrates neural networks via differentiable programming to enable inverse modeling of flow resistance and physics discovery in river channels.
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
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Solving linear-rate ODE hierarchies (like master equations) using closures and operator splitting
For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
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Scientific Machine Learning of Flow Resistance Using Universal Shallow Water Equations with Differentiable Programming
A universal shallow water equations solver integrates neural networks via differentiable programming to enable inverse modeling of flow resistance and physics discovery in river channels.
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Learning partially observed systems with neural Hamiltonian ordinary differential equations
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.