Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop a physics-inspired graph neural network (GNN) surrogate that operates directly on unstructured meshes and leverages the flexibility of graph attention. To improve both training efficiency and generalization properties of the model, we introduce a domain decomposition (DD) strategy that partitions the mesh into subdomains, trains local GNN surrogates in parallel, and aggregates their predictions. We then employ transfer learning to fine-tune models across subdomains, accelerating training and improving accuracy in data-limited settings. Applied to ice sheet simulations, our approach accurately predicts full-field velocities on high-resolution meshes, substantially reduces training time relative to training a single global surrogate model, and provides a ripe foundation for UQ objectives. Our results demonstrate that graph-based DD, combined with transfer learning, provides a scalable and reliable pathway for training GNN surrogates on massive PDE-governed systems, with broad potential for application beyond ice sheet dynamics.

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models.

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models.

Multimodal LLM-powered agents have recently demonstrated impressive capabilities in web navigation, enabling agents to complete complex browsing tasks across diverse domains. However, current agents struggle with repetitive errors and lack the ability to learn from past experiences across sessions, limiting their long-term robustness and sample efficiency. We introduce WebCoach, a model-agnostic self-evolving framework that equips web browsing agents with persistent cross-session memory, enabling improved long-term planning, reflection, and continual learning without retraining. WebCoach consists of three key components: (1) a WebCondenser, which standardizes raw navigation logs into concise summaries; (2) an External Memory Store, which organizes complete trajectories as episodic experiences; and (3) a Coach, which retrieves relevant experiences based on similarity and recency, and decides whether to inject task-specific advice into the agent via runtime hooks. This design empowers web agents to access long-term memory beyond their native context window, improving robustness in complex browsing tasks. Moreover, WebCoach achieves self-evolution by continuously curating episodic memory from new navigation trajectories, enabling agents to improve over time without retraining. Evaluations on the WebVoyager benchmark demonstrate that WebCoach consistently improves the performance of browser-use agents across three different LLM backbones. With a 38B model, it increases task success rates from 47% to 61% while reducing or maintaining the average number of steps. Notably, smaller base models with WebCoach achieve performance comparable to the same web agent using GPT-4o.

Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Y et the optimal construction of these methods requires tedious analysis and is often available only in simplified, structured-grid settings, limiting their use for more complex problems.

Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process. This difficulty can be partly explained by the spectral bias, that is, the slower convergence of high-frequency components, and can be mitigated by localizing neural networks via (overlapping) domain decomposition. We combine this localization with the Gauss-Newton method as the optimizer to obtain faster convergence than gradient-based schemes such as Adam; this comes at the cost of solving an ill-conditioned linear system in each iteration. Domain decomposition induces a block-sparse structure in the otherwise dense Gauss-Newton system, reducing the computational cost per iteration. Our numerical results indicate that combining localization and Gauss-Newton optimization is promising for neural network-based solvers for partial differential equations.

The rapid advancement of large language models(LLMs) has intensified the need for domain and culture specific evaluation. Existing benchmarks are largely Anglocentric and domain-agnostic, limiting their applicability to India-centric contexts. To address this gap, we introduce BhashaBench V1, the first domain-specific, multi-task, bilingual benchmark focusing on critical Indic knowledge systems. BhashaBench V1 contains 74,166 meticulously curated question-answer pairs, with 52,494 in English and 21,672 in Hindi, sourced from authentic government and domain-specific exams. It spans four major domains: Agriculture, Legal, Finance, and Ayurveda, comprising 90+ subdomains and covering 500+ topics, enabling fine-grained evaluation. Evaluation of 29+ LLMs reveals significant domain and language specific performance gaps, with especially large disparities in low-resource domains. For instance, GPT-4o achieves 76.49% overall accuracy in Legal but only 59.74% in Ayurveda. Models consistently perform better on English content compared to Hindi across all domains. Subdomain-level analysis shows that areas such as Cyber Law, International Finance perform relatively well, while Panchakarma, Seed Science, and Human Rights remain notably weak. BhashaBench V1 provides a comprehensive dataset for evaluating large language models across India's diverse knowledge domains. It enables assessment of models' ability to integrate domain-specific knowledge with bilingual understanding. All code, benchmarks, and resources are publicly available to support open research.