arXiv subjects

Koji Shimizu

Publications and source records attributed to Koji Shimizu.

At least 19 recordsLinked to original sources

arXiv2026

Adaptable Method for Crystal Design across Diverse Constraints and Objectives with Pretrained Property Predictors

Advanced crystal design can accelerate materials discovery across applications from photovoltaics to spintronics. Practical design must satisfy multiple properties and physical constraints, yet existing machine-learning-based approaches to such design often depend on large datasets, retraining, or task-specific generators. Here, we show that direct predictor-guided gradient optimization enables data-efficient, constraint-rich crystal design by combining off-the-shelf predictors with site-wise element masks, template initialization, and task-specific losses. In perovskites, it outperformed generative and Bayesian baselines under three targets -- band gap, formation energy, and tolerance factor -- and two hard constraints. DFT assessment further showed band-gap targeting competitive with a leading generative model despite using predictors trained on roughly one-tenth of the data. By flexibly combining pretrained predictors with application-oriented masks and custom losses, the same framework supported half-metal design. Such modularity could help researchers and engineers translate diverse application requirements directly into optimized candidate crystals with minimal computational cost.

cond-mat.mtrl-sci↗

arXiv2026

Log prismatic $F$-crystals and purity

Our goal is to study $p$-adic local systems on a rigid-analytic variety with semistable formal model. We prove that such a local system is semistable if and only if so are its restrictions to the points corresponding to the irreducible components of the special fiber. For this, the main body of the paper concerns analytic prismatic $F$-crystals on the absolute logarithmic prismatic site of a semistable $p$-adic log formal scheme. Analyzing Breuil-Kisin log prisms, we obtain a prismatic purity theorem and deduce the above purity theorem for semistable local systems.

math.NT↗

arXiv2026

A log prismatic-crystalline comparison theorem

We show a comparison theorem between log prismatic cohomology and log crystalline cohomology for a $p$-adic formal scheme with semistable reduction. Combined with the prismatic-étale comparison theorem recently proved by Tian, this implies the $C_{\mathrm{st}}$-conjecture in the semistable case with coefficients given by semistable local systems.

math.NT↗

arXiv2026

On log crystalline higher direct image

We define the big crystalline site for a log scheme and prove the basic properties. In particular, we show the boundedness, base change, and perfectness theorems for the crystalline higher direct image of quasi-coherent crystals between fine log schemes. We also introduce the big absolute crystalline sites and discuss the Frobenius isogeny property of the crystalline higher direct image of $F$-isocrystals.

math.NT↗

arXiv2025

A Straightforward Gradient-Based Approach for High-Tc Superconductor Design: Leveraging Domain Knowledge via Adaptive Constraints

Materials design aims to discover novel compounds with desired properties. However, prevailing strategies face critical trade-offs. Conventional element-substitution approaches readily and adaptively incorporate various domain knowledge but remain confined to a narrow search space. In contrast, deep generative models efficiently explore vast compositional landscapes, yet they struggle to flexibly integrate domain knowledge. To address these trade-offs, we propose a gradient-based material design framework that combines these strengths, offering both efficiency and adaptability. In our method, chemical compositions are optimised to achieve target properties by using property prediction models and their gradients. In order to seamlessly enforce diverse constraints, including those reflecting domain insights such as oxidation states, discretised compositional ratios, types of elements, and their abundance, we apply masks and employ a special loss function, namely the integer loss. Furthermore, we initialise the optimisation using promising candidates from existing dataset, effectively guiding the search away from unfavourable regions and thus helping to avoid poor solutions. Our approach demonstrates a more efficient exploration of superconductor candidates, uncovering candidate materials with higher critical temperature than conventional element-substitution and generative models. Importantly, it could propose new compositions beyond those found in existing databases, including new hydride superconductors absent from the training dataset but which share compositional similarities with materials found in literature. This synergy of domain knowledge and machine-learning-based scalability provides a robust foundation for rapid, adaptive, and comprehensive materials design for superconductors and beyond.

cond-mat.supr-con↗

arXiv2025

Moduli stacks of crystals and isocrystals

Given a liftable smooth proper variety over $\mathbb{F}_p$, we construct the moduli stacks of crystals and isocrystals on it. We show that the former is a formal algebraic stack over $\mathbb{Z}_p$ and the latter is an adic stack -- Artin stack in rigid geometry -- over $\mathbb{Q}_p$. Both stacks come equipped with the Verschiebung endomorphism $V$ corresponding to the Frobenius pullback of (iso)crystals. We study the geometry of the $V$-fixed points over the open substack of irreducible isocrystals, which we use to geometrically count the rank one $F$-isocrystals. Along the way, we carefully develop the theory of adic stacks.

math.NT↗

arXiv2024

Machine-learning potential for phonon transport in AlN with defects in multiple charge states

Understanding phonon transport properties in defect-laden AlN is important for their device applications. Here, we construct a machine-learning potential to describe phonon transport with $ab$ $initio$ accuracy in pristine and defect-laden AlN, following the template of Behler-Parrinello-type neural network potentials (NNPs) but extending them to consider multiple charge states of defects. The high accuracy of our NNP in predicting second- and third-order interatomic force constants is demonstrated through calculations of phonon bands, three-phonon anharmonic, phonon-isotope and phonon-defect scattering rates, and thermal conductivity. In particular, our NNP accurately describes the difference in phonon-related properties among various native defects and among different charge states of the defects. They reveal that the phonon-defect scattering rates induced by V$_{N}^{3+}$ are the largest, followed by V$_{Al}^{3-}$, and that V$_{N}^{1+}$ is the least effective scatterer. This is further confirmed by the magnitude of the respective depressions of the thermal conductivity of AlN. Our findings reveal the significance of the contribution from structural distortions induced by defects to the elastic scattering rates. The present work shows the usefulness of our NNP scheme to cost-efficiently study phonon transport in partially disordered crystalline phases containing charged defects.

cond-mat.mtrl-sci↗

arXiv2024

Representing Born effective charges with equivariant graph convolutional neural networks

Graph convolutional neural networks have been instrumental in machine learning of material properties. When representing tensorial properties, weights and descriptors of a physics-informed network must obey certain transformation rules to ensure the independence of the property on the choice of the reference frame. Here we explicitly encode such properties using an equivariant graph convolutional neural network. The network respects rotational symmetries of the crystal throughout by using equivariant weights and descriptors and provides a tensorial output of the target value. Applications to tensors of atomic Born effective charges in diverse materials including perovskite oxides, Li3PO4, and ZrO2, are demonstrated, and good performance and generalization ability is obtained.

cond-mat.mtrl-sci↗

arXiv2024

Completed prismatic $F$-crystals and crystalline $\mathbf{Z}_p$-local systems

We introduce the notion of completed $F$-crystals on the absolute prismatic site of a smooth $p$-adic formal scheme. We define a functor from the category of completed prismatic $F$-crystals to that of crystalline étale $\mathbf{Z}_p$-local systems on the generic fiber of the formal scheme and show that it gives an equivalence of categories. This generalizes the work of Bhatt and Scholze, which treats the case of a complete discrete valuation ring with perfect residue field.

math.NT↗

arXiv2023

Enhanced ionic conductivity through crystallization of glass-Li$_3$PS$_4$ by machine learning molecular dynamics simulations

Understanding the atomistic mechanism of ion conduction in solid electrolytes is critical for the advancement of all-solid-state batteries. Glass-ceramics, which undergo crystallization from a glass state, frequently exhibit unique properties including enhanced ionic conductivities compared to both the original crystalline and glass forms. Despite these distinctive features, specific details regarding the behavior of ion conduction in glass-ceramics, particularly concerning conduction pathways, remain elusive. In this study, we demonstrate the crystallization process of glass-Li$_3$PS$_4$ through molecular dynamics simulations employing machine learning interatomic potentials constructed from first principles calculation data. Our analyses of Li conduction using the obtained partially crystallized structures reveal that the diffusion barriers of Li decrease as the crystallinity in Li$_3$PS$_4$ glass-ceramics increases. Furthermore, Li displacements predominantly occur in the precipitated crystalline portion, suggesting that percolation conduction plays a significant role in enhanced Li conduction. These findings provide valuable insights for the future utilization of glass-ceramic materials.

cond-mat.mtrl-sci↗

arXiv2023

Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates

Deep-learning inverse techniques have attracted significant attention in recent years. Among them, the neural adjoint (NA) method, which employs a neural network surrogate simulator, has demonstrated impressive performance in the design tasks of artificial electromagnetic materials (AEM). However, the impact of the surrogate simulators' accuracy on the solutions in the NA method remains uncertain. Furthermore, achieving sufficient optimization becomes challenging in this method when the surrogate simulator is large, and computational resources are limited. Additionally, the behavior under constraints has not been studied, despite its importance from the engineering perspective. In this study, we investigated the impact of surrogate simulators' accuracy on the solutions and discovered that the more accurate the surrogate simulator is, the better the solutions become. We then developed an extension of the NA method, named Neural Lagrangian (NeuLag) method, capable of efficiently optimizing a sufficient number of solution candidates. We then demonstrated that the NeuLag method can find optimal solutions even when handling sufficient candidates is difficult due to the use of a large and accurate surrogate simulator. The resimulation errors of the NeuLag method were approximately 1/50 compared to previous methods for three AEM tasks. Finally, we performed optimization under constraint using NA and NeuLag, and confirmed their potential in optimization with soft or hard constraints. We believe our method holds potential in areas that require large and accurate surrogate simulators.

cond-mat.mtrl-sci↗

arXiv2023

Prediction of Born effective charges using neural network to study ion migration under electric fields: applications to crystalline and amorphous Li$_3$PO$_4$

Understanding ionic behaviour under external electric fields is crucial to develop electronic and energy-related devices using ion transport. In this study, we propose a neural network (NN) model to predict the Born effective charges of ions along an axis parallel to an applied electric field from atomic structures. The proposed NN model is applied to Li$_3$PO$_4$ as a prototype. The prediction error of the constructed NN model is 0.0376 $e$/atom. In combination with an NN interatomic potential, molecular dynamics (MD) simulations are performed under a uniform electric field of 0.1 V/angstrom, whereby an enhanced mean square displacement of Li along the electric field is obtained, which seems physically reasonable. In addition, the external forces along the direction perpendicular to the electric field, originating from the off-diagonal terms of the Born effective charges, are found to have a nonnegligible effect on Li migration. Finally, additional MD simulations are performed to examine the Li motion in an amorphous structure. The results reveal that Li migration occurs in various areas despite the absence of explicitly introduced defects, which may be attributed to the susceptibility of the Li ions in the local minima to the electric field. We expect that the proposed NN method can be applied to any ionic material, thereby leading to atomic-scale elucidation of ion behaviour under electric fields.

cond-mat.mtrl-sci↗

arXiv2023

Persistent homology-based descriptor for machine-learning potential of amorphous structures

High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding ab initio calculations. When applying machine-learning potentials, the construction of descriptors to represent atomic configurations is crucial. These descriptors should be invariant to symmetry operations. Handcrafted representations using a smooth overlap of atomic positions and graph neural networks (GNN) are examples of methods used for constructing symmetry-invariant descriptors. In this study, we propose a novel descriptor based on a persistence diagram (PD), a two-dimensional representation of persistent homology (PH). First, we demonstrated that the normalized two-dimensional histogram obtained from PD could predict the average energy per atom of amorphous carbon (aC) at various densities, even when using a simple model. Second, an analysis of the dimensional reduction results of the descriptor spaces revealed that PH can be used to construct descriptors with characteristics similar to those of a latent space in a GNN. These results indicate that PH is a promising method for constructing descriptors suitable for machine-learning potentials without hyperparameter tuning and deep-learning techniques.

cs.LG↗

arXiv2022

Using neural network potential to study point defect properties in multiple charge states of GaN with nitrogen vacancy

Investigation of charged defects is necessary to understand the properties of semiconductors. While density functional theory calculations can accurately describe the relevant physical quantities, these calculations increase the computational loads substantially, which often limits the application of this method to large-scale systems. In this study, we propose a new scheme of neural network potential (NNP) to analyze the point defect behavior in multiple charge states. The proposed scheme necessitates only minimal modifications to the conventional scheme. We demonstrated the prediction performance of the proposed NNP using wurzite-GaN with a nitrogen vacancy with charge states of 0, 1+, 2+, and 3+. The proposed scheme accurately trained the total energies and atomic forces for all the charge states. Furthermore, it fairly reproduced the phonon band structures and thermodynamics properties of the defective structures. Based on the results of this study, we expect that the proposed scheme can enable us to study more complicated defective systems and lead to breakthroughs in novel semiconductor applications.

cond-mat.mtrl-sci↗

arXiv2020

Phase stability of Au-Li binary systems studied using neural network potential

The miscibility of Au and Li exhibits a potential application as an adhesion layer and electrode material in secondary batteries. Here, to explore alloying properties, we constructed a neural network potential (NNP) of Au-Li binary systems based on density functional theory (DFT) calculations. To accelerate construction of NNPs, we proposed an efficient and inexpensive method of structural dataset generation. The predictions by the constructed NNP on lattice parameters and phonon properties agree well with those obtained by DFT calculations. We also investigated the mixing energy of Au$_{1-x}$Li$_{x}$ with fine composition grids, showing excellent agreement with DFT verifications. We found the existence of various compositions with structures on and slightly above the convex hull, which can explain the lack of consensus on the Au-Li stable phases in previous studies. Moreover, we newly found Au$_{0.469}$Li$_{0.531}$ as a stable phase, which has never been reported elsewhere. Finally, we examined the alloying process starting from the phase separated structure to the complete mixing phase. We found that when multiple adjacent Au atoms dissolved into Li, the alloying of the entire Au/Li interface started from the dissolved region. This paper demonstrates the applicability of NNPs toward miscible phases and provides the understanding of the alloying mechanism.

cond-mat.mtrl-sci↗

arXiv2020

A p-adic monodromy theorem for de Rham local systems

We study horizontal semistable and horizontal de Rham representations of the absolute Galois group of a certain smooth affinoid over a p-adic field. In particular, we prove that a horizontal de Rham representation becomes horizontal semistable after a finite extension of the base field. As an application, we show that every de Rham local system on a smooth rigid analytic variety becomes horizontal semistable etale locally around every classical point. We also discuss potentially crystalline loci of de Rham local systems and cohomologically potentially good reduction loci of smooth proper morphisms.

math.AG↗

arXiv2020

Perfectoid covers of abelian varieties

For an abelian variety $A$ over an algebraically closed non-archimedean field of residue characteristic $p$, we show that there exists a perfectoid space which is the tilde-limit of $\varprojlim_{[p]}A$. Our proof also works for the larger class of abeloid varieties.

math.AG↗

arXiv2017

Constancy of generalized Hodge-Tate weights of a local system

Sen attached to each p-adic Galois representation of a p-adic field a multiset of numbers called generalized Hodge-Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a p-adic local system on a rigid analytic variety over a p-adic field and show that the multiset of generalized Hodge-Tate weights of the local system is constant. The proof uses the p-adic Riemann-Hilbert correspondence by Liu and Zhu, a Sen-Fontaine decompletion theory in the relative setting, and the theory of formal connections. We also discuss basic properties of Hodge-Tate sheaves on a rigid analytic variety.

math.NT↗