arXiv subjects

Babak Sadigh

Publications and source records attributed to Babak Sadigh.

At least 19 recordsLinked to original sources

arXiv2026

Efficient method for calculation of low-temperature phase boundaries

Understanding phase stability and phase transformations is central to predicting material behavior under varying thermodynamic conditions. One of the earliest and most influential applications of density functional theory in materials science has been the prediction of pressure-induced phase transitions at 0 K. Extending these calculations to finite temperatures, however, requires accounting for thermal, quantum, and anharmonic contributions to the free energy, often at significant computational cost. In this work, we present a general and efficient framework for calculating low-temperature phase boundaries by combining the Clausius-Clapeyron equation with the quasi-harmonic approximation. This methodology requires a minimal number of calculations, while naturally incorporating internal degrees of freedom as well as quantum and low-order anharmonic effects. We illustrate the accuracy and efficiency of the approach by constructing the phase diagram of silica in the pressure range from -2 to 12 GPa and temperatures up to 1750 K. To this end, we employ a machine-learned interatomic potential trained on density functional theory reference data, enabling well-converged free energy estimates via efficient thermodynamic sampling and a rigorous comparison between the proposed framework and free energy integration.

cond-mat.mtrl-sci↗

arXiv2025

A probabilistic framework for crystal structure denoising, phase classification, and order parameters

Atomistic simulations generate large volumes of noisy structural data, yet extracting phase labels and continuous order parameters (OPs) in a robust and general manner remains challenging. Existing tools are often specialized to a limited set of prototypes and split thermal-noise removal, phase classification, and OP construction into separate steps. Here we present a unified probabilistic framework for analyzing noisy atomic configurations with respect to known crystal prototypes. The model predicts per-atom, per-prototype logits and aggregates them into a scalar log-probability (logP) landscape over atomic coordinates. Its gradient defines a conservative denoising field, while the logits provide local phase labels, prototype-resolved OPs, and ambiguity measures through logit margins. We train on AFLOW-mapped crystalline structures from the Materials Project with synthetic positional and elastic perturbations, then test extrapolation to stronger noise, finite-temperature disorder, point defects, water--ice coexistence, binary polymorphs, and shock-compressed Ti. A single differentiable scalar model recovers prototype identity after denoising, tracks smooth transformations such as Bain and Burgers paths, and exposes low-confidence regions near defects and phase boundaries. This provides an integrated and extensible tool for analyzing complex atomistic simulations.

cond-mat.mtrl-sci↗

arXiv2025

Equivalence of charged and neutral density functional formulations for correcting the many-body self-interaction of polarons

The electron self-interaction problem in density functional theory affects the accurate modeling of polarons, particularly their localization and formation energy. Charged and neutral density functional formulations have been developed to address this issue, yet their relationship remains unclear. Here, we demonstrate their equivalence in treating the many-body self-interaction of the polaron state. In particular, we connect with each other piecewise-linear functionals based on adding an extra charge to the supercell, the pSIC approach derived from the energetics of the neutral defect with polaronic distortions in a supercell, and the unit-cell method for polarons based on electron-phonon couplings. We show that these approaches lead to the same formal expression of the self-interaction corrected energy, which is fully defined by the energetics of the neutral charge state of the charged polaronic structure. Residual differences between these methods solely arise from the achieved polaronic structure, which is affected by different treatments of electron-screening and finite-size effects. We apply these methods to a set of prototypical small hole and electron polarons, including the hole polaron in MgO, the hole polaron in $\beta$-Ga$_2$O$_3$, the $V_\text{k}$ center in NaI, the electron polaron in BiVO$_4$, and the electron polaron in TiO$_2$. We show that the ground-state properties of polarons obtained using charged and neutral density functional formulations are in excellent agreement.

cond-mat.mtrl-sci↗

arXiv2025

Monte Carlo Simulations of Crystal Defects in Open Ensembles

Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian Monte Carlo method that samples energy-biased gradual transformations. The method enables free energy calculations for nonideal point defects and the direct prediction of finite-temperature interface structures.

cond-mat.mtrl-sci↗

arXiv2024

Grand canonical generative diffusion model for crystalline phases and grain boundaries

The diffusion model has emerged as a powerful tool for generating atomic structures for materials science. This work calls attention to the deficiency of current particle-based diffusion models, which represent atoms as a point cloud, in generating even the simplest ordered crystalline structures. The problem is attributed to particles being trapped in local minima during the score-driven simulated annealing of the diffusion process, similar to the physical process of force-driven simulated annealing. We develop a solution, the grand canonical diffusion model, which adopts an alternative voxel-based representation with continuous rather than fixed number of particles. The method is applied towards generation of several common crystalline phases as well as the technologically important and challenging problem of grain boundary structures.

cond-mat.mtrl-sci↗

arXiv2024

Ice phase classification made easy with score-based denoising

Accurate identification of ice phases is essential for understanding various physicochemical phenomena. However, such classification for structures simulated with molecular dynamics is complicated by the complex symmetries of ice polymorphs and thermal fluctuations. For this purpose, both traditional order parameters and data-driven machine learning approaches have been employed, but they often rely on expert intuition, specific geometric information, or large training datasets. In this work, we present an unsupervised phase classification framework that combines a score-based denoiser model with a subsequent model-free classification method to accurately identify ice phases. The denoiser model is trained on perturbed synthetic data of ideal reference structures, eliminating the need for large datasets and labeling efforts. The classification step utilizes the Smooth Overlap of Atomic Positions (SOAP) descriptors as the atomic fingerprint, ensuring Euclidean symmetries and transferability to various structural systems. Our approach achieves a remarkable 100\% accuracy in distinguishing ice phases of test trajectories using only seven ideal reference structures of ice phases as model inputs. This demonstrates the generalizability of the score-based denoiser model in facilitating phase identification for complex molecular systems. The proposed classification strategy can be broadly applied to investigate structural evolution and phase identification for a wide range of materials, offering new insights into the fundamental understanding of water and other complex systems.

cond-mat.mtrl-sci↗

arXiv2024

Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory

An accurate description of information is relevant for a range of problems in atomistic machine learning (ML), such as crafting training sets, performing uncertainty quantification (UQ), or extracting physical insights from large datasets. However, atomistic ML often relies on unsupervised learning or model predictions to analyze information contents from simulation or training data. Here, we introduce a theoretical framework that provides a rigorous, model-free tool to quantify information contents in atomistic simulations. We demonstrate that the information entropy of a distribution of atom-centered environments explains known heuristics in ML potential developments, from training set sizes to dataset optimality. Using this tool, we propose a model-free UQ method that reliably predicts epistemic uncertainty and detects out-of-distribution samples, including rare events in systems such as nucleation. This method provides a general tool for data-driven atomistic modeling and combines efforts in ML, simulations, and physical explainability.

cond-mat.mtrl-sci↗

arXiv2024

Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD timestep, which can be orders of magnitude larger than a typical MD timestep. In this work, we construct graph neural network based score dynamics models of realistic molecular systems that are evolved with 10~ps timesteps. We demonstrate the efficacy of score dynamics with case studies of alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD. Our current SD implementation is about two orders of magnitude faster than the MD counterpart for the systems studied in this work. Open challenges and possible future remedies to improve score dynamics are also discussed.

physics.comp-ph↗

arXiv2024

Accelerate Microstructure Evolution Simulation Using Graph Neural Networks with Adaptive Spatiotemporal Resolution

Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided.

cond-mat.mtrl-sci↗

arXiv2023

Spectral-partitioned Kohn-Sham density functional theory

We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact one, attaining this limit as representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for effective calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multi-projector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

physics.plasm-ph↗

arXiv2023

Score-based denoising for atomic structure identification

We propose an effective method for removing thermal vibrations that complicate the task of analyzing complex dynamics in atomistic simulation of condensed matter. Our method iteratively subtracts thermal noises or perturbations in atomic positions using a denoising score function trained on synthetically noised but otherwise perfect crystal lattices. The resulting denoised structures clearly reveal underlying crystal order while retaining disorder associated with crystal defects. Purely geometric, agnostic to interatomic potentials, and trained without inputs from explicit simulations, our denoiser can be applied to simulation data generated from vastly different interatomic interactions. The denoiser is shown to improve existing classification methods such as common neighbor analysis and polyhedral template matching, reaching perfect classification accuracy on a recent benchmark dataset of thermally perturbed structures up to the melting point. Demonstrated here in a wide variety of atomistic simulation contexts, the denoiser is general, robust, and readily extendable to delineate order from disorder in structurally and chemically complex materials.

cond-mat.mtrl-sci↗

arXiv2023

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

Accurately modeling dense plasmas over wide ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm$^3$ to 16 g/cm$^3$ and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature (SQ) method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the SESAME database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

physics.plasm-ph↗

arXiv2021

Ab initio calculations for void swelling bias in $α$ and $δ$-plutonium

Void swelling can develop in materials under persistent irradiation when non-equilibrium vacancy and self-interstitial populations migrate under sufficiently asymmetric interaction biases. In conventional metals, the propensity is determined to first approximation by comparing point-defect relaxation strains. We thus present DFT-based calculations of structures and formation energies and volumes of point defects in the $α$ and the $δ$-phases of plutonium. Our results show that lattice defects in $δ$-Pu, in contrast to most fcc metals, have surprisingly small formation volumes. Equally unexpected are the large defect formation volumes found in the low-symmetry $α$-Pu phase. Both these unusual properties can be satisfactorily explained from defect-induced spin/orbital moment formation and destruction in the Pu phases. When we use the calculated defect properties to estimate the classic void swelling bias in each of the phases, we find it to be unusually small in $δ$-Pu, but likely much larger in $α$-Pu. Hence, swelling rates and mechanisms can diverge dramatically between the different phases of Pu. Especially in the transient regime before formation of large defect clusters, the swelling rate of $α$-Pu can reliably be expected to be much larger than $δ$-Pu. However, accurate forecasts over longer times will require the conventional void-swelling theory to be modified to handle the complexities presented by the different Pu phases. As a case in point, we show possible anomalous temperature dependence of vacancy properties in $δ$-Pu, caused by entropic contributions from defect-induced spin-lattice fluctuations. Such complications may affect defect-defect interactions and thus alter the void swelling bias.

cond-mat.mtrl-sci↗

arXiv2021

Semi-Automated Creation of Density Functional Tight Binding Models Through Leveraging Chebyshev Polynomial-based Force Fields

Density Functional Tight Binding (DFTB) is an attractive method for accelerated quantum simulations of condensed matter due to its enhanced computational efficiency over standard Density Functional Theory approaches. However, DFTB models can be challenging to determine for individual systems of interest, especially for metallic and interfacial systems where different bonding arrangements can lead to significant changes in electronic states. In this regard, we have created a rapid-screening approach for determining systematically improvable DFTB interaction potentials that can yield transferable models for a variety of conditions. Our method leverages a recent reactive molecular dynamics force field where many-body interactions are represented by linear combinations of Chebyshev polynomials. This allows for the efficient creation of multi-center representations with relative ease, requiring only a small investment in initial DFT calculations. We have focused our workflow on TiH$_2$ as a model system and show that a relatively small training set based on unit-cell sized calculations yields a model accurate for both bulk and surface properties. Our approach is easy to implement and can yield accurate DFTB models over a broad range of thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.

cond-mat.mtrl-sci↗

arXiv2020

Self-Supervised Learning and Prediction of Microstructure Evolution with Recurrent Neural Networks

Microstructural evolution is a key aspect of understanding and exploiting the structure-property-performance relation of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles described by partial differential equations (PDEs). Here we demonstrate that convolutional recurrent neural networks can learn the underlying physical rules and replace PDE-based simulations in the prediction of microstructure phenomena. Neural nets are trained by self-supervised learning with image sequences from simulations of several common processes, including plane wave propagation, grain growth, spinodal decomposition and dendritic crystal growth. The trained networks can accurately predict both short-term local dynamics and long-term statistical properties of microstructures and is capable of extrapolating beyond the training datasets in spatiotemporal domains and configurational and parametric spaces. Such a data-driven approach offers significant advantages over PDE-based simulations in time stepping efficiency and offers a useful alternative especially when the material parameters or governing PDEs are not well determined.

cond-mat.mtrl-sci↗

arXiv2019

Compressive sensing lattice dynamics. II. Efficient phonon calculations and long-range interactions

We apply the compressive sensing lattice dynamics (CSLD) method to calculate phonon dispersion for crystalline solids. While existing methods such as frozen phonon, small displacement, and linear response are routinely applied for phonon calculations, they are considerable more expensive or cumbersome to apply to certain solids, including structures with large unit cells or low symmetry, systems that require more expensive electronic structure treatment, and polar semiconductors/insulators. In the latter case, we propose an approach based on a corrected long-range force constant model with proper treatment of the acoustic sum rule and the symmetric on-site force constant matrix. Our approach is demonstrated to be accurate and efficient for these systems through case studies of NaCl, CeO$_2$, Y$_3$Al$_5$O$_{12}$ and La$_2$Fe$_{14}$B.

cond-mat.mtrl-sci↗

arXiv2016

Universal scaling of the electronic and the elastic energies of small polarons revealed by high-throughput first-principles calculations

Formation of self-trapped holes (STH) in a comprehensive list of scintillator materials, including halides and chalcogenides, are studied using an accurate and computationally efficient first-principles method, the polaron self-interaction correction (pSIC). The key characteristics of small hole polarons, including their geometries, energies and degree of localization, are found vastly different from halides to oxides to systems with open-shell cations. Nevertheless, we find a universal linear relation between the energy gap separating the bound hole level from the valence band maximum and the elastic energy associated with the lattice displacement field that accompanies the polaron.

cond-mat.mtrl-sci↗

arXiv2016

Ab-initio prediction of fast non-equilibrium transport of nascent polarons in SrI$_2$: A key to high-performance scintillation

The excellent light yield proportionality of europium-doped strontium iodide (SrI$_2$:Eu) has resulted in state-of-the-art $γ$-ray detectors with remarkably high energy resolution, far exceeding that of most halide compounds. In this class of materials the formation of self-trapped hole polarons is very common. However, polaron formation is usually expected to limit carrier mobilities and has been associated with poor scintillator light-yield proportionality and resolution. Here, using a recently developed first-principles method, we perform an unprecedented study of polaron transport in SrI$_2$, both for equilibrium polarons, as well as nascent polarons immediately following a self-trapping event. As a result, we put forward a rationale for the unexpected high energy resolution of SrI$_2$. We identify nine stable hole polaron configurations, which consist of dimerized iodine pairs with polaron binding energies of up to 0.5\,eV. They are connected by a complex potential energy landscape that comprises 66 unique nearest-neighbor migration paths. \textit{Ab initio} molecular dynamics simulations reveal that a large fraction of polarons is born into configurations that migrate practically barrier free at room temperature. As a result, carriers created during $γ$-irradiation can quickly diffuse away reducing the chance for non-linear recombination reactions that are the primary culprits for non-proportionality and resolution reduction. This leads to the conclusion that the flat, albeit complex, landscape for polaron migration in SrI$_2$ is key for understanding its outstanding performance. This insight provides important guidance not only for the future development of high-performance scintillators but also of other materials, for which large polaron mobilities are crucial such as batteries and solid state ionic conductors.

cond-mat.mtrl-sci↗