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Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…

Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the polynomial order in the computational mesh when using high-order solvers.…

This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…

Parameter-efficient transfer learning (PETL) has become a promising paradigm for adapting large-scale vision foundation models to downstream tasks. Typical methods primarily leverage the intrinsic low rank property to make decomposition,…

Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle…

Building on existing $hp$-adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propose a novel $h$-adaptive algorithm for a fixed polynomial…

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…

Demand forecasting in competitive, uncertain business environments requires models that can integrate multiple evaluation perspectives rather than being restricted to hyperparameter optimization based on a single metric. This traditional…

Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…

Despite the significant breakthrough of Mixture-of-Experts (MoE), the increasing scale of these MoE models presents huge memory and storage challenges. Existing MoE pruning methods, which involve reducing parameter size with a uniform…

Autonomous assembly is an essential capability for industrial and service robots, with Peg-in-Hole (PiH) insertion being one of the core tasks. However, PiH assembly in unknown environments is still challenging due to uncertainty in task…

Pre-trained Language Models (PLMs) have demonstrated their superiority and versatility in modern Natural Language Processing (NLP), effectively adapting to various downstream tasks through further fine-tuning. Federated Parameter-Efficient…

In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…

Model merging has recently emerged as a lightweight alternative to ensembling, combining multiple fine-tuned models into a single set of parameters with no additional training overhead. Yet, existing merging methods fall short of matching…

We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…

Designing effective heuristics for NP-hard combinatorial optimization problems remains challenging and often requires substantial domain expertise. Recent LLM-guided evolutionary methods have shown promise for automated heuristic…

In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a…

High precision assembly of mechanical parts requires accuracy exceeding the robot precision. Conventional part mating methods used in the current manufacturing requires tedious tuning of numerous parameters before deployment. We show how…

Large Language Models (LLMs) have advanced the field of Combinatorial Optimization through automated heuristic generation. Instead of relying on manual design, this LLM-Driven Heuristic Design (LHD) process leverages LLMs to iteratively…