Adam P. Generale, Andreas E. Robertson, Surya R. Kalidindi
Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of probability distributions representing possible outcomes of a specific process, existing frameworks cannot satisfactorily account for the impact of conditioning variables on these dynamics. Amongst several limitations, existing methods require training data with paired conditions and are developed for discrete conditioning variables. We propose Conditional Variable Flow Matching (CVFM), a framework for learning flows transforming conditional distributions with amortization across continuous conditioning variables - permitting predictions across the conditional density manifold. This is accomplished through several novel advances. In particular, simultaneous sample conditioned flows over the main and conditioning variables, alongside a conditional Wasserstein distance combined with a loss reweighting kernel facilitating conditional optimal transport. Collectively, these advances allow for learning system dynamics provided measurement data whose states and conditioning variables are not in correspondence. We demonstrate CVFM on a suite of increasingly challenging problems, including discrete and continuous conditional mapping benchmarks, image-to-image domain transfer, and modeling the temporal evolution of materials internal structure during manufacturing processes. We observe that CVFM results in improved performance and convergence characteristics over alternative conditional variants.
Pranoy Ray, Adam P. Generale, Nikhith Vankireddy et al.
Molecular Dynamics (MD) simulations are essential for accurately predicting the physical and chemical properties of large molecular systems across various pressure and temperature ensembles. However, the high computational costs associated with All-Atom (AA) MD simulations have led to the development of Coarse-Grained Molecular Dynamics (CGMD), providing a lower-dimensional compression of the AA structure into representative CG beads, offering reduced computational expense at the cost of predictive accuracy. Existing CGMD methods, such as CG-Martini (calibrated against experimental data), aim to generate an embedding of a topology that sufficiently generalizes across a range of structures. Detrimentally, in attempting to specify parameterization with applicability across molecular classes, it is unable to specialize to domain-specific applications, where sufficient accuracy and computational speed are critical. This work presents a novel approach to optimize derived results from CGMD simulations by refining the general-purpose Martini3 topologies specifically the bonded interaction parameters within a given coarse-grained mapping - for domain-specific applications using Bayesian Optimization methodologies. We have developed and validated a CG potential applicable to any degree of polymerization, representing a significant advancement in the field. Our optimized CG potential, based on the Martini3 framework, aims to achieve accuracy comparable to AAMD while maintaining the computational efficiency of CGMD. This approach bridges the gap between efficiency and accuracy in multiscale molecular simulations, potentially enabling more rapid and cost-effective molecular discovery across various scientific and technological domains.
Michael Buzzy, Andreas Robertson, Peng Chen et al.
Recent advances in Foundation Models for Materials Science are poised to revolutionize the discovery, manufacture, and design of novel materials with tailored properties and responses. Although great strides have been made, successes have been restricted to materials classes where multi-million sample data repositories can be readily curated (e.g., atomistic structures). Unfortunately, for many structural and functional materials (e.g., mesoscale structured metal alloys), such datasets are too costly or prohibitive to construct; instead, datasets are limited to very few examples. To address this challenge, we introduce a novel machine learning approach for learning from hyper-sparse, complex spatial data in scientific domains. Our core contribution is a physics-driven data augmentation scheme that leverages an ensemble of local generative models, trained on as few as five experimental observations, and coordinates them through a novel diversity curation strategy to generate a large-scale, physically diverse dataset. We utilize this framework to construct PolyMicros, the first Foundation Model for polycrystalline materials (a structural material class important across a broad range of industrial and scientific applications). We demonstrate the utility of PolyMicros by zero-shot solving several long standing challenges related to accelerating 3D experimental microscopy. Finally, we make both our models and datasets openly available to the community.
Hooman Danesh, Maruthi Annamaraju, Tim Brepols et al.
The capabilities of additive manufacturing have facilitated the design and production of mechanical metamaterials with diverse unit cell geometries. Establishing linkages between the vast design space of unit cells and their effective mechanical properties is critical for the efficient design and performance evaluation of such metamaterials. However, physics-based simulations of metamaterial unit cells across the entire design space are computationally expensive, necessitating a materials informatics framework to efficiently capture complex structure-property relationships. In this work, principal component analysis of 2-point correlation functions is performed to extract the salient features from a large dataset of randomly generated 2D metamaterials. Physics-based simulations are performed using a fast Fourier transform (FFT)-based homogenization approach to efficiently compute the homogenized effective elastic stiffness across the extensive unit cell designs. Subsequently, Gaussian process regression is used to generate reduced-order surrogates, mapping unit cell designs to their homogenized effective elastic constant. It is demonstrated that the adopted workflow enables a high-value low-dimensional representation of the voluminous stochastic metamaterial dataset, facilitating the construction of robust structure-property maps. Finally, an uncertainty-based active learning framework is utilized to train a surrogate model with a significantly smaller number of data points compared to the original full dataset. It is shown that a dataset as small as $0.61\%$ of the entire dataset is sufficient to generate accurate and robust structure-property maps.
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major computational bottleneck using traditional numerical solvers. Furthermore, machine learning methods such as neural operators struggle to fit these maps due to sharp transitions and high contrast in the coefficient fields and a scarcity of informative training data. In this work, we focus on a canonical problem in computational mechanics: prediction of local elastic deformation fields over heterogeneous material structures subjected to periodic boundary conditions. We construct a hybrid approximation for the coefficient-to-solution map using a Thermodynamically-informed Iterative Neural Operator (TherINO). Rather than using coefficient fields as direct inputs and iterating over a learned latent space, we employ thermodynamic encodings -- drawn from the constitutive equations -- and iterate over the solution space itself. Through an extensive series of case studies, we elucidate the advantages of these design choices in terms of efficiency, accuracy, and flexibility. We also analyze the model's stability and extrapolation properties on out-of-distribution coefficient fields and demonstrate an improved speed-accuracy tradeoff for predicting elastic quantities of interest.
Prathik R Kaundinya, Kamal Choudhary, Surya R. Kalidindi
Machine learning (ML) based models have greatly enhanced the traditional materials discovery and design pipeline. Specifically, in recent years, surrogate ML models for material property prediction have demonstrated success in predicting discrete scalar-valued target properties to within reasonable accuracy of their DFT-computed values. However, accurate prediction of spectral targets such as the electron Density of States (DOS) poses a much more challenging problem due to the complexity of the target, and the limited amount of available training data. In this study, we present an extension of the recently developed Atomistic Line Graph Neural Network (ALIGNN) to accurately predict DOS of a large set of material unit cell structures, trained to the publicly available JARVIS-DFT dataset. Furthermore, we evaluate two methods of representation of the target quantity - a direct discretized spectrum, and a compressed low-dimensional representation obtained using an autoencoder. Through this work, we demonstrate the utility of graph-based featurization and modeling methods in the prediction of complex targets that depend on both chemistry and directional characteristics of material structures.
The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e. physics based) or data-driven (i.e. machine-learning based) origins. In order to combine the strengths of these two approaches, we advance a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. In this paradigm, a given problem is converted into an equivalent L-S equation and solved as an optimization problem, where the optimization procedure is calibrated to the problem at hand. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. This architecture leverages the generalizability and computational efficiency of machine learning approaches, but also permits a physics-based interpretation. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains. Since numerous governing equations can be converted into an equivalent L-S form, the proposed architecture has potential applications across a range of multiscale materials phenomena.