Ryo Igarashi

Yoshitomo Matsubara, Naoya Chiba, Ryo Igarashi et al.

This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling ranges of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. We also create another 120 datasets that contain dummy variables to examine whether SR methods can choose necessary variables only. Besides, we propose to use normalized edit distances (NED) between a predicted equation and the true equation trees for addressing a critical issue that existing SR metrics are either binary or errors between the target values and an SR model's predicted values for a given input. We conduct benchmark experiments on our new SRSD datasets using various representative SR methods. The experimental results show that we provide a more realistic performance evaluation, and our user study shows that the NED correlates with human judges significantly more than an existing SR metric. We publish repositories of our code and 240 SRSD datasets.

Naoya Chiba, Yuta Suzuki, Tatsunori Taniai et al.

Representing crystal structures of materials to facilitate determining them via neural networks is crucial for enabling machine-learning applications involving crystal structure estimation. Among these applications, the inverse design of materials can contribute to explore materials with desired properties without relying on luck or serendipity. We propose neural structure fields (NeSF) as an accurate and practical approach for representing crystal structures using neural networks. Inspired by the concepts of vector fields in physics and implicit neural representations in computer vision, the proposed NeSF considers a crystal structure as a continuous field rather than as a discrete set of atoms. Unlike existing grid-based discretized spatial representations, the NeSF overcomes the tradeoff between spatial resolution and computational complexity and can represent any crystal structure. We propose an autoencoder of crystal structures that can recover various crystal structures, such as those of perovskite structure materials and cuprate superconductors. Extensive quantitative results demonstrate the superior performance of the NeSF compared with the existing grid-based approach.

Michiko Yoshitake, Yuta Suzuki, Ryo Igarashi et al.

We present MaterialFigBench, a benchmark dataset designed to evaluate the ability of multimodal large language models (LLMs) to solve university-level materials science problems that require accurate interpretation of figures. Unlike existing benchmarks that primarily rely on textual representations, MaterialFigBench focuses on problems in which figures such as phase diagrams, stress-strain curves, Arrhenius plots, diffraction patterns, and microstructural schematics are indispensable for deriving correct answers. The dataset consists of 137 free-response problems adapted from standard materials science textbooks, covering a broad range of topics including crystal structures, mechanical properties, diffusion, phase diagrams, phase transformations, and electronic properties of materials. To address unavoidable ambiguity in reading numerical values from images, expert-defined answer ranges are provided where appropriate. We evaluate several state-of-the-art multimodal LLMs, including ChatGPT and GPT models accessed via OpenAI APIs, and analyze their performance across problem categories and model versions. The results reveal that, although overall accuracy improves with model updates, current LLMs still struggle with genuine visual understanding and quantitative interpretation of materials science figures. In many cases, correct answers are obtained by relying on memorized domain knowledge rather than by reading the provided images. MaterialFigBench highlights persistent weaknesses in visual reasoning, numerical precision, and significant-digit handling, while also identifying problem types where performance has improved. This benchmark provides a systematic and domain-specific foundation for advancing multimodal reasoning capabilities in materials science and for guiding the development of future LLMs with stronger figure-based understanding.

Michiko Yoshitake, Yuta Suzuki, Ryo Igarashi et al.

A college-level benchmark dataset for large language models (LLMs) in the materials science field, MaterialBENCH, is constructed. This dataset consists of problem-answer pairs, based on university textbooks. There are two types of problems: one is the free-response answer type, and the other is the multiple-choice type. Multiple-choice problems are constructed by adding three incorrect answers as choices to a correct answer, so that LLMs can choose one of the four as a response. Most of the problems for free-response answer and multiple-choice types overlap except for the format of the answers. We also conduct experiments using the MaterialBENCH on LLMs, including ChatGPT-3.5, ChatGPT-4, Bard (at the time of the experiments), and GPT-3.5 and GPT-4 with the OpenAI API. The differences and similarities in the performance of LLMs measured by the MaterialBENCH are analyzed and discussed. Performance differences between the free-response type and multiple-choice type in the same models and the influence of using system massages on multiple-choice problems are also studied. We anticipate that MaterialBENCH will encourage further developments of LLMs in reasoning abilities to solve more complicated problems and eventually contribute to materials research and discovery.

Tatsunori Taniai, Ryo Igarashi, Yuta Suzuki et al.

Predicting physical properties of materials from their crystal structures is a fundamental problem in materials science. In peripheral areas such as the prediction of molecular properties, fully connected attention networks have been shown to be successful. However, unlike these finite atom arrangements, crystal structures are infinitely repeating, periodic arrangements of atoms, whose fully connected attention results in infinitely connected attention. In this work, we show that this infinitely connected attention can lead to a computationally tractable formulation, interpreted as neural potential summation, that performs infinite interatomic potential summations in a deeply learned feature space. We then propose a simple yet effective Transformer-based encoder architecture for crystal structures called Crystalformer. Compared to an existing Transformer-based model, the proposed model requires only 29.4% of the number of parameters, with minimal modifications to the original Transformer architecture. Despite the architectural simplicity, the proposed method outperforms state-of-the-art methods for various property regression tasks on the Materials Project and JARVIS-DFT datasets.

Florian Lalande, Yoshitomo Matsubara, Naoya Chiba et al.

Symbolic Regression (SR) searches for mathematical expressions which best describe numerical datasets. This allows to circumvent interpretation issues inherent to artificial neural networks, but SR algorithms are often computationally expensive. This work proposes a new Transformer model aiming at Symbolic Regression particularly focused on its application for Scientific Discovery. We propose three encoder architectures with increasing flexibility but at the cost of column-permutation equivariance violation. Training results indicate that the most flexible architecture is required to prevent from overfitting. Once trained, we apply our best model to the SRSD datasets (Symbolic Regression for Scientific Discovery datasets) which yields state-of-the-art results using the normalized tree-based edit distance, at no extra computational cost.

Yusei Ito, Tatsunori Taniai, Ryo Igarashi et al.

Crystal structure modeling with graph neural networks is essential for various applications in materials informatics, and capturing SE(3)-invariant geometric features is a fundamental requirement for these networks. A straightforward approach is to model with orientation-standardized structures through structure-aligned coordinate systems, or"frames." However, unlike molecules, determining frames for crystal structures is challenging due to their infinite and highly symmetric nature. In particular, existing methods rely on a statically fixed frame for each structure, determined solely by its structural information, regardless of the task under consideration. Here, we rethink the role of frames, questioning whether such simplistic alignment with the structure is sufficient, and propose the concept of dynamic frames. While accommodating the infinite and symmetric nature of crystals, these frames provide each atom with a dynamic view of its local environment, focusing on actively interacting atoms. We demonstrate this concept by utilizing the attention mechanism in a recent transformer-based crystal encoder, resulting in a new architecture called CrystalFramer. Extensive experiments show that CrystalFramer outperforms conventional frames and existing crystal encoders in various crystal property prediction tasks.

Yuta Suzuki, Tatsunori Taniai, Ryo Igarashi et al.

Understanding structure-property relationships is an essential yet challenging aspect of materials discovery and development. To facilitate this process, recent studies in materials informatics have sought latent embedding spaces of crystal structures to capture their similarities based on properties and functionalities. However, abstract feature-based embedding spaces are human-unfriendly and prevent intuitive and efficient exploration of the vast materials space. Here we introduce Contrastive Language--Structure Pre-training (CLaSP), a learning paradigm for constructing crossmodal embedding spaces between crystal structures and texts. CLaSP aims to achieve material embeddings that 1) capture property- and functionality-related similarities between crystal structures and 2) allow intuitive retrieval of materials via user-provided description texts as queries. To compensate for the lack of sufficient datasets linking crystal structures with textual descriptions, CLaSP leverages a dataset of over 400,000 published crystal structures and corresponding publication records, including paper titles and abstracts, for training. We demonstrate the effectiveness of CLaSP through text-based crystal structure screening and embedding space visualization.