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11 records

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DOE OSTI2023

Saddle point search with dynamic active volume

Sampling potential energy surface (PES) is critical for many problems in materials science, chemistry, physics, and biology and requires highly efficient saddle point searches (SPS). In the study, we introduce the concept of dynamic active volume (DAV) in addition to the active volume in self-evolving atomistic kinetic Monte Carlo (SEAKMC). The DAV method has further reduced the dimensionality of the PES at the elevation stage of a SPS. At the subsequent converging stage, the dynamic boundary in DAV is lifted to allow the system to converge to the right location of a saddle point. Coupled with the dimer method, the DAV method not only significantly reduces the time cost for a given search attempt, but also dramatically increases the probability of finding relevant saddle points for PES sampling. Further, a Python software package within the framework SEAKMC (SEAKMC_py) with the DAV method has been developed.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Discovery of multimechanisms of screw dislocation interaction in bcc iron from open-ended saddle point searches

Dislocation motion and interactions determine mechanical properties in body-centered cubic (bcc) metallic materials. However, studying mechanisms for the screw dislocation interaction is fundamentally challenging since many underlying processes involve mesotimescales and atomistic resolution, currently inaccessible by either experimental techniques or continuum theoretical methods. Here, in this paper, we develop a computational capability based on self-evolving atomistic kinetic Monte Carlo (SEAKMC) to sample the critical events and saddle point energies related to screw dislocations and their junctions. The method is first validated by calculating the stress dependence of Peierls barriers and formation energies of kink pairs and cross-slip kink pairs on a single screw dislocation in bcc iron. Then the method is applied to a binary junction of a pair of intersecting screw dislocations, the structure of which is crucial for low-temperature plastic deformation. We identify three important mechanisms: coplanar cross-slipping, jog-pinning, and a previously unknown unzipping mechanism during the evolution of the binary junction. The mechanisms are then further validated using classical molecular dynamics simulations. The computational capability developed in this paper provides an effective tool to evaluate screw dislocation related thermally activated events in complex stress conditions. The mechanisms discovered in this paper provide critical insights into temperature dependence of the anomalous slip, a breakdown of the Schmidt law, during the plastic deformation in bcc iron and can be generalized to other bcc metals.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Atomistic modeling of meso -timescale processes with $\mathrm{SEAKMC}$: A perspective and recent developments

On-the-fly kinetic Monte Carlo (kMC) methods have recently garnered significant attentions after successful applications to various atomic-scale problems using a timescale outside the reach of classical molecular dynamics. These methods play a critical role in modeling atomistic meso-timescale processes, and it is therefore essential to further improve their capabilities. In this report we review one of the on-the-fly kMC methods, Self-Evolving Atomistic kinetic Monte Carlo (SEAKMC) and propose two schemes that considerably enhance the efficiency of saddle point searches (SPSs) during the simulations. The performance of these schemes is tested using the diffusion of point defects in bcc Fe. In addition, we discuss approaches to significantly mitigate limitations of these schemes, which further improves their efficiencies. Importantly, these schemes improve the SPS efficiency not only for SEAKMC but also for other on-the-fly kMC methods, broadening the applications of on-the-fly kMC simulations to complex meso-timescale problems.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Pynta-An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. Here, we present Pynta, a workflow software for automating the calculation of surface and gas–surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Saddle point sampling using scaled normal coordinates

The sampling of saddle points (SPs) on a potential energy surface (PES) is critical for describing the dynamics and transport properties of materials. In this paper we propose a saddle point search (SPS) method that enables efficient sampling of practically meaningful SPs around a local minimum by converting the PES to the scaled normal coordinates (SNCs), together with the dimer method. We find that the pathway leading to a SP using SNCs is highly efficient and is independent of the system size. This results in the significantly increased SPS efficiency and the enhanced possibility of a complete catalog of the SPs. In addition, we perform SPSs using the SNCs for the diffusion of a vacancy and a dumbbell in body-centered cubic Fe and demonstrate (1) the required number of system force evaluations for a SPS decreases by at least an order of magnitude, (2) the effects of the system size on the number of force evaluations are greatly decreased, and (3) the effects of the number of atoms involved in the SPS on the probability of finding practically meaningful SPs is mostly eliminated. We also discuss the computational cost of introducing the SNCs. It should be highlighted that the SNCs could also be applied to other minimum-mode following methods, demonstrating the general versatility of the proposed method.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Atomistic learning in the electronically grand-canonical ensemble

Abstract A strategy is presented for the machine-learning emulation of electronic structure calculations carried out in the electronically grand-canonical ensemble. The approach relies upon a dual-learning scheme, where both the system charge and the system energy are predicted for each image. The scheme is shown to be capable of emulating basic electrochemical reactions at a range of potentials, and coupling it with a bootstrap-ensemble approach gives reasonable estimates of the prediction uncertainty. The method is also demonstrated to accelerate saddle-point searches, and to extrapolate to systems with one to five water layers. We anticipate that this method will allow for larger length- and time-scale simulations necessary for electrochemical simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2020

CRNT4SBML: a Python package for the detection of bistability in biochemical reaction networks

Motivation: Signaling pathways capable of switching between two states are ubiquitous within living organisms. They provide the cells with the means to produce reversible or irreversible decisions. Switchlike behavior of biological systems is realized through biochemical reaction networks capable of having two or more distinct steady states which are dependent on initial conditions. Investigation of whether a certain signaling pathway can confer bistability involves a substantial amount of hypothesis testing. The cost of direct experimental testing can be prohibitive. Therefore, constraining the hypothesis space is highly bene?cial. One such methodology is based on Chemical Reaction Network Theory which uses computational techniques to rule out pathways that are not capable of bistability regardless of kinetic constant values and molecule concentrations. Although useful, these methods are complicated from both pureandcomputationalmathematicsperspectives.Thus,theiradoptionisverylimitedamongstbiologists. Results: We brought Chemical Reaction Network Theory approaches closer to experimental biologists by automating all the necessary steps in CRNT4SMBL. The input is based on SBML format which is the community standard for biological pathway communication. The tool parses SBML and derives C-graph representations of the biological pathway with mass action kinetics. Next steps involve an ef?cient search for potential saddle-node bifurcation points using an optimization technique. This type of bifurcation is important as it has the potential of acting as a switching point between two steady states. Finally, if any bifurcation points are present, numerical continuation analysis extends the equilibria branches for generating the diagram. Presence of an S-shaped bifurcation diagram indicates that the pathway acts as a bistable switch for the given optimization parameters. Availability: CRNT4SBML is available via the Python Package Index. The documentation can be found at https://crnt4sbml.readthedocs.io. CRNT4SBML is licensed under the Apache Software License 2.0. Contact: vladislav.petyuk@pnnl.gov

Reyes, Brandon C.↗

DOE OSTI2026

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗

DOE OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Iyer, Gopal R.↗

NASA NTRS2001

Electron-Impact Ionization of Methane

We report a study of the total ionization of CH_4 by electron impact and its dissociative ionization from the ^2T_2 channel. The calculation of the total ionization cross section uses the improved Binary-Encounter-Dipole model (iBED).(W. A Huo, Phys. Rev. A (submitted for publication).) The dipole Born cross section in the model is expressed in terms of a three-term representation and the optical oscillator strengths are taken from Backx and Van der Wiel.(C. Backx and M. J. Van der Wiel, I Phys. B 18) 3020 (1975). The nuclear dynamics for the dissociation of the ^2T_2 channel is studied using the statistical model. A search of the potential energy surface of the ^2T_2 state of CH_4^+ shows two minima, of C_2v and C_3v symmetries, in agreement with earlier calculations. ((a) K. Takeshita, J. Chem. Phys. 86), 329 (1987). (b) R. F. Frey and E. R. Davidson, J. Chem. Phys. 88, 1775 (1988). The dissociation of the CH_4^+ to CH_3^+ + H goes through a saddle point. Comparison with recent experimental data will be presented and the role of Jahn-Teller effect discussed.

Huo, Winifred M.↗