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Dec 12

Facet: highly efficient E(3)-equivariant networks for interatomic potentials

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.

  • 9 authors
·
Sep 10

LLM-enabled Instance Model Generation

In the domain of model-based engineering, models are essential components that enable system design and analysis. Traditionally, the creation of these models has been a manual process requiring not only deep modeling expertise but also substantial domain knowledge of target systems. With the rapid advancement of generative artificial intelligence, large language models (LLMs) show potential for automating model generation. This work explores the generation of instance models using LLMs, focusing specifically on producing XMI-based instance models from Ecore metamodels and natural language specifications. We observe that current LLMs struggle to directly generate valid XMI models. To address this, we propose a two-step approach: first, using LLMs to produce a simplified structured output containing all necessary instance model information, namely a conceptual instance model, and then compiling this intermediate representation into a valid XMI file. The conceptual instance model is format-independent, allowing it to be transformed into various modeling formats via different compilers. The feasibility of the proposed method has been demonstrated using several LLMs, including GPT-4o, o1-preview, Llama 3.1 (8B and 70B). Results show that the proposed method significantly improves the usability of LLMs for instance model generation tasks. Notably, the smaller open-source model, Llama 3.1 70B, demonstrated performance comparable to proprietary GPT models within the proposed framework.

  • 5 authors
·
Mar 28

MM-Agent: LLM as Agents for Real-world Mathematical Modeling Problem

Mathematical modeling is a cornerstone of scientific discovery and engineering practice, enabling the translation of real-world problems into formal systems across domains such as physics, biology, and economics. Unlike mathematical reasoning, which assumes a predefined formulation, modeling requires open-ended problem analysis, abstraction, and principled formalization. While Large Language Models (LLMs) have shown strong reasoning capabilities, they fall short in rigorous model construction, limiting their utility in real-world problem-solving. To this end, we formalize the task of LLM-powered real-world mathematical modeling, where agents must analyze problems, construct domain-appropriate formulations, and generate complete end-to-end solutions. We introduce MM-Bench, a curated benchmark of 111 problems from the Mathematical Contest in Modeling (MCM/ICM), spanning the years 2000 to 2025 and across ten diverse domains such as physics, biology, and economics. To tackle this task, we propose MM-Agent, an expert-inspired framework that decomposes mathematical modeling into four stages: open-ended problem analysis, structured model formulation, computational problem solving, and report generation. Experiments on MM-Bench show that MM-Agent significantly outperforms baseline agents, achieving an 11.88\% improvement over human expert solutions while requiring only 15 minutes and \$0.88 per task using GPT-4o. Furthermore, under official MCM/ICM protocols, MM-Agent assisted two undergraduate teams in winning the Finalist Award (top 2.0\% among 27,456 teams) in MCM/ICM 2025, demonstrating its practical effectiveness as a modeling copilot. Our code is available at https://github.com/usail-hkust/LLM-MM-Agent

  • 6 authors
·
May 20

A Survey on Mixture of Experts

Large language models (LLMs) have garnered unprecedented advancements across diverse fields, ranging from natural language processing to computer vision and beyond. The prowess of LLMs is underpinned by their substantial model size, extensive and diverse datasets, and the vast computational power harnessed during training, all of which contribute to the emergent abilities of LLMs (e.g., in-context learning) that are not present in small models. Within this context, the mixture of experts (MoE) has emerged as an effective method for substantially scaling up model capacity with minimal computation overhead, gaining significant attention from academia and industry. Despite its growing prevalence, there lacks a systematic and comprehensive review of the literature on MoE. This survey seeks to bridge that gap, serving as an essential resource for researchers delving into the intricacies of MoE. We first briefly introduce the structure of the MoE layer, followed by proposing a new taxonomy of MoE. Next, we overview the core designs for various MoE models including both algorithmic and systemic aspects, alongside collections of available open-source implementations, hyperparameter configurations and empirical evaluations. Furthermore, we delineate the multifaceted applications of MoE in practice, and outline some potential directions for future research. To facilitate ongoing updates and the sharing of cutting-edge developments in MoE research, we have established a resource repository accessible at https://github.com/withinmiaov/A-Survey-on-Mixture-of-Experts.

  • 6 authors
·
Jun 26, 2024

Efficient Self-Supervised Learning for Earth Observation via Dynamic Dataset Curation

Self-supervised learning (SSL) has enabled the development of vision foundation models for Earth Observation (EO), demonstrating strong transferability across diverse remote sensing tasks. While prior work has focused on network architectures and training strategies, the role of dataset curation, especially in balancing and diversifying pre-training datasets, remains underexplored. In EO, this challenge is amplified by the redundancy and heavy-tailed distributions common in satellite imagery, which can lead to biased representations and inefficient training. In this work, we propose a dynamic dataset pruning strategy designed to improve SSL pre-training by maximizing dataset diversity and balance. Our method iteratively refines the training set without requiring a pre-existing feature extractor, making it well-suited for domains where curated datasets are limited or unavailable. We demonstrate our approach on the Sentinel-1 Wave Mode (WV) Synthetic Aperture Radar (SAR) archive, a challenging dataset dominated by ocean observations. We train models from scratch on the entire Sentinel-1 WV archive spanning 10 years. Across three downstream tasks, our results show that dynamic pruning improves both computational efficiency and representation quality, leading to stronger transferability. We also release the weights of Nereus-SAR-1, the first model in the Nereus family, a series of foundation models for ocean observation and analysis using SAR imagery, at github.com/galeio-research/nereus-sar-models/.

  • 5 authors
·
Apr 9