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cs.NE updates on arXiv.org

MPCS: Neuroplastic Continual Learning via Multi-Component Plasticity and Topology-Aware EWC Combining Trained Models in Reinforcement Learning Training Non-Differentiable Networks via Optimal Transport ShiftLIF: Efficient Multi-Level Spiking Neurons with Power-of-Two Quantization Probe-Geometry Alignment: Erasing the Cross-Sequence Memorization Signature Below Chance Benchmarking local Hebbian learning rules for memory storage and prototype extraction Robust volatility updates for Hierarchical Gaussian Filtering Spiking Sequence Machines and Transformers Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts Scalable Learning in Structured Recurrent Spiking Neural Networks without Backpropagation Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks Attractor FCM Physical Foundation Models: Fixed hardware implementations of large-scale neural networks When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry Learning to Forget: Continual Learning with Adaptive Weight Decay Causal Learning with Neural Assemblies NORACL: Neurogenesis for Oracle-free Resource-Adaptive Continual Learning Text-Utilization for Encoder-dominated Speech Recognition Models EdgeSpike: Spiking Neural Networks for Low-Power Autonomous Sensing in Edge IoT Architectures EvoTSC: Evolving Feature Learning Models for Time Series Classification via Genetic Programming Analysis and Explainability of LLMs Via Evolutionary Methods Deployment-Aligned Low-Precision Neural Architecture Search for Spaceborne Edge AI SeaEvo: Advancing Algorithm Discovery with Strategy Space Evolution Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs MAEO: Multiobjective Animorphic Ensemble Optimization for Scalable Large-scale Engineering Applications Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks Learn&Drop: Fast Learning of CNNs based on Layer Dropping Architecture-Induced Recoverability Bias in Differentiable Symbolic Regression Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen Structure-Guided Diffusion Model for EEG-Based Visual Cognition Reconstruction
Hermite Neural Network Simulation for Solving the 2D Schr...
Kourosh Parand, Aida Pakniyat · 2024-02-16 · via cs.NE updates on arXiv.org

The Schrodinger equation is a mathematical equation describing the wave function's behavior in a quantum-mechanical system. It is a partial differential equation that provides valuable insights into the fundamental principles of quantum mechanics. In this paper, the aim was to solve the Schrodinger equation with sufficient accuracy by using a mixture of neural networks with the collocation method base Hermite functions. Initially, the Hermite functions roots were employed as collocation points, enhancing the efficiency of the solution. The Schrodinger equation is defined in an infinite domain, the use of Hermite functions as activation functions resulted in excellent precision. Finally, the proposed method was simulated using MATLAB's Simulink tool. The results were then compared with those obtained using Physics-informed neural networks and the presented method.