PVD-ONet combines multi-network DeepONet modules with Prandtl and Van Dyke matching conditions to map initial data to solution operators for families of singularly perturbed boundary-layer problems and to infer scaling exponents from sparse observations.
Extended Ph ysics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
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Oscillatory state-space models with PDE-aware spectral bases are introduced as inductive biases for PINNs, yielding improved accuracy and lower memory on forward, inverse, and up to 100D PDE tasks.
HSPINN enforces Dirichlet and periodic BCs exactly via analytical lifting and masking, applies adaptive softmax weighting to soft loss terms for PDE residuals, and reports faster convergence and higher accuracy than standard PINNs on Poisson, Burgers, and convection problems.
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.
Admissible negative-w_r branches of trace-quadratic f(R,T) black holes support axial ringdown spectra governed by a single master equation equivalent to Einstein gravity plus frozen anisotropic fluid, differing from Schwarzschild by ~22% with no resolved α dependence.
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Auto-Adaptive PINNs with Applications to Phase Transitions
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.