Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly …
Gradient-based training and pruning for radial basis function networks in materials physics.
problem Interpretable and robust machine learning for materials physics problems.
method Gradient-based training and pruning of radial basis function networks with closed-form optimization criteria.
result Pruned models provide compact and interpretable versions of larger models, offering insights into atom-level migration processes.
We enhance autonomous materials research with problem-aware models.
problem Complex decision-making in autonomous materials.
method Bayesian framework, machine learning, physics-based models, operational considerations.
result Improved models reflect problem-specific structure.
Explains isometric immersions and their applications.
problem Isometric immersions and their applications in math and physics.
method Historical overview and applications.
result Explains the importance and applications of isometric immersions.
Physics-constrained GP predicts material states under shockwave conditions.
problem Predicting material states under extreme shockwave conditions.
method Physics-constrained Gaussian Process regression with Rankine-Hugoniot constraints.
result Reproduces Hugoniot curves with satisfactory accuracy and uncertainty quantification.
ML PCA detects phase transitions in muon spectroscopy data.
problem Detecting phase transitions in materials using muon spectroscopy data.
method Unsupervised Machine Learning (PCA) applied to asymmetry functions.
result PCA method effectively detects phase transitions in muon spectroscopy experiments.
A key problem in computational material science deals with understanding the effect of material distribution (i.e., microstructure) on material performance. The challenge is to synthesize microstructures, given a finite number of microstructure images, and/or some physical invariances that the microstructure exhibits. …
Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first and second case the investigation is reduced to the analysis of the nonidentical …
PCA improves detection of phase transitions in muon spectroscopy data from various materials.
problem Subtle changes in asymmetry function indicate phase transitions, but existing methods require material-specific knowledge.
method Applied unsupervised PCA to muon spectroscopy asymmetry data from multiple materials.
result PCA can recover phase transition indicators and improve detection of material-specific variations.
PANIS learns PDE surrogates for heterogeneous materials without solving the PDE.
problem Learning surrogates for parametrized PDEs in heterogeneous media.
method Physics-aware neural implicit solvers combining probabilistic learning and physics-informed discretization.
result Learned surrogates for effective solutions in heterogeneous materials without solving the reference problem.
Method reveals dissimilarity in alloys' Curie temperatures.
problem Tackles the dissimilarity between rare-earth transition metal binary alloys.
method Ensemble learning with Kernel ridge regression.
result Reveals meaningful relations between alloys' structure and Curie temperature.
Although Bayesian Optimization (BO) has been employed for accelerating materials design in computational materials engineering, existing works are restricted to problems with quantitative variables. However, real designs of materials systems involve both qualitative and quantitative design variables representing materi…
Paper introduces ML tools for guided wave behaviour in composite materials.
problem Difficult assessment of guided wave behaviour in complex materials.
method Data-driven model using Gaussian processes with physical constraints.
result Structured machine learning models offer advantages like extrapolation and physical interpretation.
Reduced order modeling of energetic materials using physics-aware neural networks.
problem Simulating complex spatiotemporal dynamics in energetic materials.
method Physics-aware recurrent convolutions (PARC) combined with latent space projection to accelerate model training and inference.
result Significant decrease in training and inference time with comparable accuracy.
Neural model predicts object states and physical parameters from visual observations.
problem Computational models struggle with physical reasoning and adapting to new environments.
method Visual prior predicts particle-based system from visual observations; inference module refines estimates subject to dynamics constraints.
result Model can infer physical properties within a few observations and adapt to unseen scenarios.
TANNs integrate thermodynamics into ANN models for accurate, consistent predictions.
problem Lack of rigorous physics-based approach in ANN constitutive modeling.
method TANNs encode thermodynamics principles in neural network architecture using automatic differentiation.
result TANNs produce thermodynamically consistent predictions without requiring large datasets.
Extracts important peaks from XRD spectra using Attention mechanism.
problem Identifying significant peaks in XRD patterns for material properties.
method Convolutional neural network with Attention mechanism to analyze deep features.
result Selected lattice constant predicts cathodic material cell voltage.
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by Partial Differential Equation (PDE), and its loading/ response mapping can be solve…
Parsimonious neural networks discover interpretable physical laws from data.
problem Discovering interpretable physical laws from data using machine learning.
method Combining neural networks with evolutionary optimization to balance accuracy and parsimony.
result Developed models for classical mechanics and materials melting temperature prediction.
Symmetry-electronic fingerprints reveal competing magnetic phases in two-dimensional materials.
problem Predicting magnetic ground states, moments, and anisotropy in two-dimensional magnets.
method Introduce the symmetry-electronic fingerprint (SEF), a physically interpretable representation that encodes crystallographic symmetry operations, Wyckoff-site geometry, and site-resolved electronic structure.
result SEF-trained models accurately classify magnetic ordering and regress moments alongside anisotropy energies.
Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature space be identified to allow reconstruction of new designs, and (2) the reconstructi…
4-dim intrinsic (material) Riemannian metric G of the material 4-D space-time continuum P is utilized as the characteristic of the aging processes developing in the material. Manifested through variation of basic material characteristics such as density, moduli of elasticity, yield stress, strength, and toughness.,…
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…
Generative models improve digital twins for structures with uncertainties.
problem Uncertainty in structural modelling limits deterministic models.
method Two types of generative models: physics-based SFE and data-driven cGANs.
result Data-driven cGANs outperform physics-based models in nonlinear structures.
MPM-ParVI uses particle sampling for variational inference.
problem Variational inference for complex probabilistic models.
method Material Point Method (MPM) for particle-based simulation.
result Deterministic sampling and inference for intractable densities.
Gopakumar-Vafa large N duality is a correspondence between Chern-Simons invariants of a link in a 3-manifold and relative Gromov-Witten invariants of a 6-dimensional symplectic manifold relative to a Lagrangian submanifold. We address the correspondence between the Chern-Simons free energy of S^3 with no link and the G…
Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework …
Robot science discovers new materials faster.
problem Discovering advanced materials in complex synthesis landscapes.
method Closed-loop, active learning-driven autonomous system.
result Discovery of a novel epitaxial nanocomposite phase-change memory material.
These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of Mathematics, Kyoto University.
Geometric GNNs model 3D atomic systems with rotations and translations.
problem Modeling 3D atomic systems with geometric graphs and machine learning.
method Invariant, equivariant, and unconstrained GNN architectures.
result Geometric GNNs leverage physical symmetries and chemical properties.
A field theory is constructed in the context of parameterized absolute parallelism geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the geometric structure of the geometry used (the parallelization vector fields). Three t…
A hybrid model combines diffusion and neural operator methods for stress prediction in hyperelastic materials.
problem Challenges in predicting stress fields in hyperelastic materials with complex microstructures.
method A hybrid surrogate framework combining a conditional denoising diffusion probabilistic model (cDDPM) and a modified DeepONet.
result The hybrid model consistently outperforms traditional methods by one to two orders of magnitude.
Physics-informed GANs estimate elastic moduli from mechanical tests.
problem Estimating spatially-varying elastic moduli from measured deformations.
method Physics-informed Generative Adversarial Networks (PI-GANs) with PDE constraints.
result Generated stiffness samples match true distribution statistics.
The goal of this article is to give an elementary introduction to Dirac geometry and group-valued moment maps, via pure spinors. The material is based on my lectures at the summer school on 'Poisson geometry in Mathematics and Physics' at Keio University, June 2006.
The answers to many unsolved problems lie in the intractable chemical space of molecules and materials. Machine learning techniques are rapidly growing in popularity as a way to compress and explore chemical space efficiently. One of the most important aspects of machine learning techniques is representation through th…
New method generates equilibrium glass configurations efficiently.
problem Sampling equilibrium configurations of amorphous materials is slow and difficult.
method Riemannian stochastic interpolation framework combining Riemannian stochastic interpolant and equivariant flow matching.
result Enforcing geometric and symmetry constraints significantly improves generative performance.
Deep learning excels in AI but struggles with causal physics.
problem Deep learning struggles with causal relationships in physical sciences.
method Combining Bayesian methods, physical constraints, and causal models.
result Deep learning can mislead in systems with unclear causal relationships.
A neural network speeds up bond-associated peridynamics simulations.
problem High computational costs in bond-associated peridynamics.
method Message-passing neural network (MPNN) for bond-associated peridynamic material correspondence formulation.
result Significantly reduces computation time via GPU acceleration.
Defines observer-invariant time derivatives on moving surfaces.
problem Deriving appropriate definitions for time derivatives on surfaces that move.
method Systematically derived from spacetime settings, considering observer-invariance and covariance principles.
result Formulations applicable for computations of tangential n-tensor fields on moving surfaces.
The paper tackles inverse uncertainty quantification in neutron noise analysis.
problem Uncertainty in estimating material properties from noisy neutron correlation measurements.
method Surrogate models and inverse uncertainty quantification to account for measurement error and model bias.
result Improved prediction of neutron correlations and quantification of uncertainties.
Study pentagon growth with laser-cut models.
problem Explore topological and geometric properties of pentagon cell growth.
method Cell growth process in Euclidean plane, physical representations created with laser cutter.
result Aesthetic and geometric insights from pentagon growth models.
The paper develops tensor learning methods exploiting symmetries of tensor functions.
problem Efficiently handling tensors in various scientific contexts.
method Equivariant machine learning architectures exploiting orthogonal, Lorentz, and symplectic symmetries.
result Equivariant models outperform non-equivariant baselines in time series analysis.
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in terms of the horizontal (characteristic) cohomology. Applications to computing invar…
New method finds graphene nanocrystals with reduced DFT calculations.
problem Efficiently discovering materials with desired properties in high-dimensional chemical space.
method Bayesian optimization with neural network kernel to minimize DFT calculations.
result Reduced computational cost by 20% for discovering materials with target properties.
Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media,…
Develops a nonlocal PINN framework using PDDO for better solution of PDEs with sharp gradients.
problem Dealing with sharp gradients in solutions of PDEs using traditional PINN approaches.
method Integrates long-range interactions (nonlocality) into PINN using Peridynamic Differential Operator (PDDO).
result Nonlocal PINN approach improves solution accuracy and parameter inference for problems with sharp gradients.
Gryffin optimizes categorical variables in materials design, leveraging expert knowledge.
problem Optimizing categorical variables in complex design choices like molecule selection.
method Bayesian optimization with smooth approximations to categorical distributions, incorporating expert knowledge.
result Gryffin accelerates discovery of promising molecules and materials, highlighting relevant correlations.
Model predicts stable molecules with AI and physics constraints.
problem Designing stable molecules with limited data.
method Graph Scattering Variational Autoencoder with physical constraints.
result Model generates stable molecules with desired properties.