We develop a flexible framework based on physics-informed neural networks for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By encoding the underlying physical laws into the loss function and designing network architectures that incorporate the singular behavior and dynamic boundaries, our approach enables robust and accurate solutions to both ordinary and partial differential equations with complex boundary conditions. We demonstrate the versatility of this framework through applications to minimal surface problems in anti-de Sitter (AdS) spacetime, including examples relevant to the AdS/CFT correspondence (e.g. Wilson loops and gluon scattering amplitudes) popularly used in the context of string theory in theoretical physics. Our methods efficiently handle singularities at boundaries, and also support both ‘soft’ (loss-based) and ‘hard’ (formulation-based) imposition of boundary conditions, including cases where the position of a boundary is promoted to a trainable parameter. The techniques developed here are not limited to high-energy theoretical physics but are broadly applicable to boundary value problems encountered in mathematics, engineering, and the natural sciences, wherever singularities and moving boundaries play a critical role.
We study the instanton effect on the gluon scattering amplitudes at strong coupling and large N for the 𝒩 = 4 supersymmetric Yang-Mills theory. According to Alday and Maldacena, the gluon scattering amplitude corresponds holographically to the area of a worldsheet minimal surface in the T-dual AdS5 geometry. The Yang-Mills instanton introduces an instanton D-brane in the geometry, with which a particular boundary condition for the minimal surface is imposed. We show that the minimal surface undergoes a topology change depending on the size and the gluon momenta, and that the instanton amplitude exhibits a characteristic dependence on gluon momenta. More specifically, we find that when the fixed instanton size modulus ρ is larger than 𝒪(√(λ)/E) where λ is the ’t Hooft coupling and E is the typical momentum of the scattering gluon, due to the topology change of the worldsheet minimal surface, the instanton amplitude is exponentially enhanced as exp(ρE).
Spiking neural networks (SNNs) provide an energy-efficient framework for neuromorphic computing, but their performance is often constrained by limited architectural flexibility and catastrophic forgetting in continual learning. To address these issues, we propose GRSNN, a graph-wired spiking neural network for neuromorphic classification and continual learning. GRSNN combines a convolution–temporal accumulated batch normalization–spike triplet for stable spatiotemporal representation learning, a directed acyclic graph backbone for flexible multi-route propagation and feature fusion, and a spike attention module for adaptive enhancement of informative spike responses. In addition, a critical path-based preservation mechanism is introduced to identify and stabilize task-relevant computational paths during sequential learning, thereby improving the balance between plasticity and stability. Experiments on N-Caltech101, DVS-Gesture, and CIFAR10-DVS show that GRSNN achieves strong classification performance under different simulation timesteps. Continual learning results on both similar-task and dissimilar-task settings further demonstrate its effectiveness in reducing forgetting while maintaining competitive adaptation. Moreover, GRSNN achieves lower computational energy and shorter training time, indicating a favorable trade-off between accuracy, robustness, and efficiency. Overall, this work highlights the effectiveness of graph-wired path-level learning for building flexible and reliable SNNs in dynamic learning scenarios.
Room-temperature sonication in water converts CaCO 3 /Ca(OH) 2 into CNO-enriched carbons with 20–30 nm concentric shells via atmospheric CO 2 capture.
