AD-RaNN learns an effective low-dimensional sampling distribution for hidden parameters in randomized neural networks by optimizing a vector p via PDE-driven or data-driven adaptation and a two-stage least-squares procedure, improving accuracy on benchmark PDE problems.
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature Machine Intelligence, 3(3):218–229
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GTransNet extends single-hidden-layer TransNet by adding hidden layers with symmetry-constrained biases and variance-controlled weights to improve accuracy and stability for oscillatory steady-state PDE solutions.
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Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework
AD-RaNN learns an effective low-dimensional sampling distribution for hidden parameters in randomized neural networks by optimizing a vector p via PDE-driven or data-driven adaptation and a two-stage least-squares procedure, improving accuracy on benchmark PDE problems.
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Generalized Transferable Neural Networks for Steady-State Partial Differential Equations
GTransNet extends single-hidden-layer TransNet by adding hidden layers with symmetry-constrained biases and variance-controlled weights to improve accuracy and stability for oscillatory steady-state PDE solutions.