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194 records · Page 11

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Near-optimal ground state preparation

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

97 MATHEMATICS AND COMPUTING↗

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A scalable multidimensional fully implicit solver for Hall magnetohydrodynamics

We propose an optimally performant fully implicit algorithm for the Hall magnetohydrodynamics (HMHD) equations based on multigrid-preconditioned Jacobian-free Newton-Krylov methods. HMHD is a challenging system to solve numerically because it supports stiff fast dispersive waves. The preconditioner is formulated using an operator-split approximate block factorization (Schur complement), informed by physics insight. We use a vector-potential formulation (instead of a magnetic field one) to allow a clean segregation of the problematic $\nabla$ x $\nabla$ x operator in the electron Ohm's law subsystem. This segregation allows the formulation of an effective damped block-Jacobi smoother for multigrid. We demonstrate by analysis that our proposed block-Jacobi iteration is convergent and has the smoothing property. The resulting HMHD solver is verified linearly with wave propagation examples, and nonlinearly with the GEM challenge reconnection problem by comparison against another HMHD code. We demonstrate the excellent algorithmic and parallel performance of the algorithm up to 16384 MPI tasks in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

Efficiently embedding QUBO problems on adiabatic quantum computers

Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. Yet, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. Here, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.

97 MATHEMATICS AND COMPUTING↗

Computing molecular excited states on a D-Wave quantum annealer

Abstract The possibility of using quantum computers for electronic structure calculations has opened up a promising avenue for computational chemistry. Towards this direction, numerous algorithmic advances have been made in the last five years. The potential of quantum annealers, which are the prototypes of adiabatic quantum computers, is yet to be fully explored. In this work, we demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience. The excited states are treated using two methods, time-dependent Hartree–Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm–Dancoff approximation (TDA). The resulting TDA eigenvalue equations are solved on a D-Wave quantum annealer using the Quantum Annealer Eigensolver (QAE), developed previously. The method is shown to reproduce a typical basis set convergence on the example $$\hbox {H}_2$$ H 2 molecule and is also applied to several other molecular species. Characteristic properties such as transition dipole moments and oscillator strengths are computed as well. Three potential energy profiles for excited states are computed for $$\hbox {NH}_3$$ NH 3 as a function of the molecular geometry. Similar to previous studies, the accuracy of the method is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv.

74 ATOMIC AND MOLECULAR PHYSICS↗

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations that do not have performance guarantees. We propose and analyze a nonvariational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electronic structure of mononuclear Cu-based molecule from density-functional theory with self-interaction correction

In this paper, we investigate the electronic structure of a planar mononuclear Cu-based molecule [Cu(C 6 H 4 S 2 ) 2 ] z in two oxidation states ( z = –2, –1) using density-functional theory (DFT) with Fermi–Löwdin orbital (FLO) self-interaction correction (SIC). The dianionic Cu-based molecule was proposed to be a promising qubit candidate. Self-interaction error within approximate DFT functionals renders severe delocalization of electron and spin densities arising from 3 d orbitals. The FLO-SIC method relies on optimization of Fermi–Löwdin orbital descriptors (FODs) with which localized occupied orbitals are constructed to create SIC potentials. Starting with many initial sets of FODs, we employ a frozen-density loop algorithm within the FLO-SIC method to study the Cu-based molecule. We find that the electronic structure of the molecule remains unchanged despite somewhat different final FOD configurations. In the dianionic state (spin S = 1/2), FLO-SIC spin density originates from the Cu d and S p orbitals with an approximate ratio of 2:1, in quantitative agreement with multireference calculations, while in the case of SIC-free DFT, the orbital ratio is reversed. Overall, FLO-SIC lowers the energies of the occupied orbitals and, in particular, the 3 d orbitals unhybridized with the ligands significantly, which substantially increases the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) compared to SIC-free DFT results. The FLO-SIC HOMO–LUMO gap of the dianionic state is larger than that of the monoanionic state, which is consistent with experiment. Our results suggest a positive outlook of the FLO-SIC method in the description of magnetic exchange coupling within 3 d -element-based systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Application of Simulated Annealing and Related Algorithms to TWTA Design

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Radke, Eric M.↗

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Collective neutrino oscillations in three flavors on qubit and qutrit processors

Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions, which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and Advanced Quantum Testbed device at the Lawrence Berkeley National Laboratory for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. Finally, while hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphysical qubit space, unlike the qubit setup.

Neutrino oscillations↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗