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Memory-Guided Trust-Region Bayesian Optimization (MG-TuRBO) for High Dimensions EngageTriBoost: Predictive Modeling of User Engagement in Digital Mental Health Intervention Using Explainable Machine Learning Reservoir observer enhanced with residual calibration and attention mechanism Efficient RL Training for LLMs with Experience Replay Wireless Communication Enhanced Value Decomposition for Multi-Agent Reinforcement Learning Adversarial Sensor Errors for Safe and Robust Wind Turbine Fleet Control IKKA: Inversion Classification via Critical Anomalies for Robust Visual Servoing Adaptive Simulation Experiment for LLM Policy Optimization EvoLen: Evolution-Guided Tokenization for DNA Language Model Smartwatch-Based Sitting Time Estimation in Real-World Office Settings Structural Evaluation Metrics for SVG Generation via Leave-One-Out Analysis Loom: A Scalable Analytical Neural Computer Architecture Spectral Geometry of LoRA Adapters Encodes Training Objective and Predicts Harmful Compliance Finite-Sample Analysis of Nonlinear Independent Component Analysis:Sample Complexity and Identifiability Bounds How does Chain of Thought decompose complex tasks? 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Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition Unified Multimodal Uncertain Inference EfficientSign: An Attention-Enhanced Lightweight Architecture for Indian Sign Language Recognition Skip-Connected Policy Optimization for Implicit Advantage PRAGMA: Revolut Foundation Model 3D-VCD: Hallucination Mitigation in 3D-LLM Embodied Agents through Visual Contrastive Decoding Creator Incentives in Recommender Systems: A Cooperative Game-Theoretic Approach for Stable and Fair Collaboration in Multi-Agent Bandits Evidential Transformation Network: Turning Pretrained Models into Evidential Models for Post-hoc Uncertainty Estimation StructRL: Recovering Dynamic Programming Structure from Learning Dynamics in Distributional Reinforcement Learning Generative 3D Gaussian Splatting for Arbitrary-ResolutionAtmospheric Downscaling and Forecasting From Selection to Scheduling: Federated Geometry-Aware Correction Makes Exemplar Replay Work Better under 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Evaluating Escalation Behavior in Automation with Language Models Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation On the Spectral Geometry of Cross-Modal Representations: A Functional Map Diagnostic for Multimodal Alignment Structured Exploration and Exploitation of Label Functions for Automated Data Annotation MolPaQ: Modular Quantum-Classical Patch Learning for Interpretable Molecular Generation CausalVAD: De-confounding End-to-End Autonomous Driving via Causal Intervention Reinforcement-aware Knowledge Distillation for LLM Reasoning SubQuad: Near-Quadratic-Free Structure Inference with Distribution-Balanced Objectives in Adaptive Receptor framework A Horizon-Aware Decision-Support Framework for Demand Forecasting Model Selection in Resilient Production Planning Measurement-Consistent Langevin Corrector for Stabilizing Latent Diffusion Inverse Problem Solvers Multi-agent Adaptive Mechanism Design When & How to Write for Personalized Demand-aware Query Rewriting in Video Search Relational Visual Similarity From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity On-the-Fly Adaptation to Quantization: Configuration-Aware LoRA for Efficient Fine-Tuning of Quantized LLMs STCast: Adaptive Boundary Alignment for Global and Regional Weather Forecasting OmniPrism: Learning Disentangled Visual Concept for Image Generation FIT-GNN: Faster Inference Time for GNNs that 'FIT' in Memory Using Coarsening
Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion
Ariel Neufeld, Philipp Schmocker · 2024-11-06 · via cs.LG updates on arXiv.org

In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their corresponding solution. Moreover, we provide some approximation rates for learning the solution of SPDEs with additive and/or multiplicative noise. Finally, we apply our results in numerical examples to approximate the solution of three SPDEs: the stochastic heat equation, the Heath-Jarrow-Morton equation, and the Zakai equation.

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