LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models

Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorized forms, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy. These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.

Generative Latent Neural PDE Solver using Flow Matching

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion probabilistic model has been shown to enhance the temporal stability of neural solvers, while its stochastic inference mechanism enables ensemble predictions and uncertainty quantification. In principle, such training involves sampling a series of discretized diffusion timesteps during both training and inference, inevitably increasing computational overhead. In addition, most diffusion models apply isotropic Gaussian noise on structured, uniform grids, limiting their adaptability to irregular domains. We propose a latent diffusion model for PDE simulation that embeds the PDE state in a lower-dimensional latent space, which significantly reduces computational costs. Our framework uses an autoencoder to map different types of meshes onto a unified structured latent grid, capturing complex geometries. By analyzing common diffusion paths, we propose to use a coarsely sampled noise schedule from flow matching for both training and testing. Numerical experiments show that the proposed model outperforms several deterministic baselines in both accuracy and long-term stability, highlighting the potential of diffusion-based approaches for robust data-driven PDE learning.

Protein Structure-Function Relationship: A Kernel-PCA Approach for Reaction Coordinate Identification

In this study, we propose a Kernel-PCA model designed to capture structure-function relationships in a protein. This model also enables ranking of reaction coordinates according to their impact on protein properties. By leveraging machine learning techniques, including Kernel and principal component analysis (PCA), our model uncovers meaningful patterns in high-dimensional protein data obtained from molecular dynamics (MD) simulations. The effectiveness of our model in accurately identifying reaction coordinates has been demonstrated through its application to a G protein-coupled receptor. Furthermore, this model utilizes a network-based approach to uncover correlations in the dynamic behavior of residues associated with a specific protein property. These findings underscore the potential of our model as a powerful tool for protein structure-function analysis and visualization.

NANOGPT: A Query-Driven Large Language Model Retrieval-Augmented Generation System for Nanotechnology Research

This paper presents the development and application of a Large Language Model Retrieval-Augmented Generation (LLM-RAG) system tailored for nanotechnology research. The system leverages the capabilities of a sophisticated language model to serve as an intelligent research assistant, enhancing the efficiency and comprehensiveness of literature reviews in the nanotechnology domain. Central to this LLM-RAG system is its advanced query backend retrieval mechanism, which integrates data from multiple reputable sources. The system retrieves relevant literature by utilizing Google Scholar's advanced search, and scraping open-access papers from Elsevier, Springer Nature, and ACS Publications. This multifaceted approach ensures a broad and diverse collection of up-to-date scholarly articles and papers. The proposed system demonstrates significant potential in aiding researchers by providing a streamlined, accurate, and exhaustive literature retrieval process, thereby accelerating research advancements in nanotechnology. The effectiveness of the LLM-RAG system is validated through rigorous testing, illustrating its capability to significantly reduce the time and effort required for comprehensive literature reviews, while maintaining high accuracy, query relevance and outperforming standard, publicly available LLMS.

AdditiveLLM: Large Language Models Predict Defects in Additive Manufacturing

In this work we investigate the ability of large language models to predict additive manufacturing defect regimes given a set of process parameter inputs. For this task we utilize a process parameter defect dataset to fine-tune a collection of models, titled AdditiveLLM, for the purpose of predicting potential defect regimes including Keyholing, Lack of Fusion, and Balling. We compare different methods of input formatting in order to gauge the model's performance to correctly predict defect regimes on our sparse Baseline dataset and our natural language Prompt dataset. The model displays robust predictive capability, achieving an accuracy of 93\% when asked to provide the defect regimes associated with a set of process parameters. The incorporation of natural language input further simplifies the task of process parameters selection, enabling users to identify optimal settings specific to their build.

Modeling Melt Pool Features and Spatter Using Symbolic Regression and Machine Learning

Additive manufacturing (AM) is a rapidly evolving technology that has attracted applications across a wide range of fields due to its ability to fabricate complex geometries. However, one of the key challenges in AM is achieving consistent print quality. This inconsistency is often attributed to uncontrolled melt pool dynamics, partly caused by spatter which can lead to defects. Therefore, capturing and controlling the evolution of the melt pool is crucial for enhancing process stability and part quality. In this study, we developed a framework to support decision-making in AM operations, facilitating quality control and minimizing defects via machine learning (ML) and polynomial symbolic regression models. We implemented experimentally validated computational tools as a cost-effective approach to collect large datasets from laser powder bed fusion (LPBF) processes. For a dataset consisting of 281 process conditions, parameters such as melt pool dimensions (length, width, depth), melt pool geometry (area, volume), and volume indicated as spatter were extracted. Using machine learning (ML) and polynomial symbolic regression models, a high R2 of over 95 % was achieved in predicting the melt pool dimensions and geometry features for both the training and testing datasets, with either process conditions (power and velocity) or melt pool dimensions as the model inputs. In the case of volume indicated as spatter, R2 improved after logarithmic transforming the model inputs, which was either the process conditions or the melt pool dimensions. Among the investigated ML models, the ExtraTree model achieved the highest R2 values of 96.7 % and 87.5 %.

Text to Band Gap: Pre-trained Language Models as Encoders for Semiconductor Band Gap Prediction

In this study, we explore the use of a transformer-based language model as an encoder to predict the band gaps of semiconductor materials directly from their text descriptions. Quantum chemistry simulations, including Density Functional Theory (DFT), are computationally intensive and time-consuming, which limits their practicality for high-throughput material screening, particularly for complex systems. Shallow machine learning (ML) models, while effective, often require extensive data preprocessing to convert non-numerical material properties into numerical inputs. In contrast, our approach leverages textual data directly, bypassing the need for complex feature engineering. We generate material descriptions in two formats: formatted strings combining features and natural language text generated using the ChatGPT API. We demonstrate that the RoBERTa model, pre-trained on natural language processing tasks, performs effectively as an encoder for prediction tasks. With minimal fine-tuning, it achieves a mean absolute error (MAE) of approximately 0.33 eV, performing better than shallow machine learning models such as Support Vector Regression, Random Forest, and XGBoost. Even when only the linear regression head is trained while keeping the RoBERTa encoder layers frozen, the accuracy remains nearly identical to that of the fully trained model. This demonstrates that the pre-trained RoBERTa encoder is highly adaptable for processing domain-specific text related to material properties, such as the band gap, significantly reducing the need for extensive retraining. This study highlights the potential of transformer-based language models to serve as efficient and versatile encoders for semiconductor materials property prediction tasks.

Dual Diffusion for Unified Image Generation and Understanding

Diffusion models have gained tremendous success in text-to-image generation, yet still lag behind with visual understanding tasks, an area dominated by autoregressive vision-language models. We propose a large-scale and fully end-to-end diffusion model for multi-modal understanding and generation that significantly improves on existing diffusion-based multimodal models, and is the first of its kind to support the full suite of vision-language modeling capabilities. Inspired by the multimodal diffusion transformer (MM-DiT) and recent advances in discrete diffusion language modeling, we leverage a cross-modal maximum likelihood estimation framework that simultaneously trains the conditional likelihoods of both images and text jointly under a single loss function, which is back-propagated through both branches of the diffusion transformer. The resulting model is highly flexible and capable of a wide range of tasks including image generation, captioning, and visual question answering. Our model attained competitive performance compared to recent unified image understanding and generation models, demonstrating the potential of multimodal diffusion modeling as a promising alternative to autoregressive next-token prediction models.

Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a black box by directly predicting the next state. While this is a natural and easy framework for applying neural surrogates, it can be an over-simplified and rigid framework for predicting physics. In this work, we propose an alternative framework in which neural solvers predict the temporal derivative and an ODE integrator forwards the solution in time, which has little overhead and is broadly applicable across model architectures and PDEs. We find that by simply changing the training target and introducing numerical integration during inference, neural surrogates can gain accuracy and stability. Predicting temporal derivatives also allows models to not be constrained to a specific temporal discretization, allowing for flexible time-stepping during inference or training on higher-resolution PDE data. Lastly, we investigate why this new framework can be beneficial and in what situations does it work well.

Planning and Reasoning with 3D Deformable Objects for Hierarchical Text-to-3D Robotic Shaping

Deformable object manipulation remains a key challenge in developing autonomous robotic systems that can be successfully deployed in real-world scenarios. In this work, we explore the challenges of deformable object manipulation through the task of sculpting clay into 3D shapes. We propose the first coarse-to-fine autonomous sculpting system in which the sculpting agent first selects how many and where to place discrete chunks of clay into the workspace to create a coarse shape, and then iteratively refines the shape with sequences of deformation actions. We leverage large language models for sub-goal generation, and train a point cloud region-based action model to predict robot actions from the desired point cloud sub-goals. Additionally, our method is the first autonomous sculpting system that is a real-world text-to-3D shaping pipeline without any explicit 3D goals or sub-goals provided to the system. We demonstrate our method is able to successfully create a set of simple shapes solely from text-based prompting. Furthermore, we explore rigorously how to best quantify success for the text-to-3D sculpting task, and compare existing text-image and text-point cloud similarity metrics to human evaluations for this task. For experimental videos, human evaluation details, and full prompts, please see our project website: https://sites.google.com/andrew.cmu.edu/hierarchicalsculpting