Related papers: HypeR Adaptivity: Joint $hr$-Adaptive Meshing via …

The adaptation of large language models (LLMs) to specialized reasoning tasks is fundamentally constrained by computational resources. Parameter-Efficient Fine-Tuning (PEFT) methods have emerged as a powerful solution, yet the landscape of…

We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

Foundation models excel across diverse tasks, but adapting them to specialized applications often requires fine-tuning, an approach that is memory and compute-intensive. Parameter-efficient fine-tuning (PEFT) methods mitigate this by…

Continual learning is an essential capability of human cognition, yet it poses significant challenges for current deep learning models. The primary issue is that new knowledge can interfere with previously learned information, causing the…

This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

Hierarchical reinforcement learning (HRL) has the potential to solve complex long horizon tasks using temporal abstraction and increased exploration. However, hierarchical agents are difficult to train due to inherent non-stationarity. We…

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

Referring Expression Comprehension (REC), which aims to ground a local visual region via natural language, is a task that heavily relies on multimodal alignment. Most existing methods utilize powerful pre-trained models to transfer…

This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…

Hyperparameter selection is critical for stable and efficient convergence of heterogeneous federated learning, where clients differ in computational capabilities, and data distributions are non-IID. Tuning hyperparameters is a manual and…

Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…

Deep reinforcement learning has recently emerged as a promising feedback control strategy for complex dynamical systems governed by partial differential equations (PDEs). When dealing with distributed, high-dimensional problems in state and…

We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop…

Recent advances in multimodal large reasoning models (MLRMs) have substantially improved their ability to solve complex textual and visual tasks. However, these models tend to overthink on simple problems, producing unnecessarily lengthy…

Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

Multi-modal models excel in cross-modal tasks but are computationally expensive due to their billions of parameters. Parameter-efficient fine-tuning (PEFT) offers a solution by adding small trainable components while freezing pre-trained…