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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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We provide the final report for this grant, detailing the publications, software produced, students trained who have joined the DOE workforce, and the impact our work has had on computational mathematics and related disciplines.
Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.
Scientific software used on high-performance computing platforms is in a phase of transformation because of the combined increase in the heterogeneity and complexity of models and hardware platforms. Having separate implementations for different platforms can easily lead to combinatorial explosions; therefore, the computational science community has been looking for mechanisms to express code through abstractions that can be specialized for different platforms. Most existing approaches use template meta-programming in C++, and are, therefore language specific. Here, we have developed a tool that uses customized expansion of macros to mimic some of C++ behavior in other languages. It enables unification of any code variants that may be necessary to run efficiently on different target architectures and different computational environments through use of macros with multiple alternative definitions and ability to arbitrate on definition selection for expansion. Combined with two other tools, a custom runtime, and a user specified recipe translator, our custom macroprocessor becomes a part of an overall performance portability solution that does not depend on any specific programming language. We also use macros as code-shorthand that lets code snippets become building blocks that allow variations in control flow to explore performance options. We demonstrate use of macros in Flash-X, a multiphysics multicomponent code with many Fortran legacy components derived from an earlier community code FLASH.
Satellites provide essential services such as networking and weather tracking, and the number of near-earth and deep space satellites are expected to grow rapidly in the coming years. Communications with terrestrial ground stations is one of the critical functionalities of any space mission. Satellite scheduling is a problem that has been scientifically investigated since the 1970s. A central aspect of this problem is the need to consider resource contention and satellite visibility constraints as they require line of sight. Due to the combinatorial nature of the problem, prior solutions such as linear programs and evolutionary algorithms require extensive compute capabilities to output a feasible schedule for each scenario. Machine learning based scheduling can provide an alternative solution by training a model with historical data and generating a schedule quickly with model inference. We present SatNet, a benchmark for satellite scheduling optimization based on historical data from the NASA Deep Space Network. We propose formulation of the satellite scheduling problem as a Markov Decision Process and use reinforcement learning (RL) policies to generate schedules. The nature of constraints imposed by SatNet differ from other combinatorial optimization problems such as vehicle routing studied in prior literature. Our initial results indicate that RL is an alternative optimization approach that can generate candidate solutions of comparable quality to existing state-of-the-practice results. However, we also find that RL policies overfit to the training dataset and do not generalize well to new data, thereby necessitating continued research on reusable and generalizable agents.
Discovering novel catalysts requires complex reasoning involving multiple chemical properties and resultant trade-offs, leading to a combinatorial growth in the search space. While large language models (LLM) have demonstrated novel capabilities for chemistry through complex instruction following capabilities and high quality reasoning, a goal-driven combinatorial search using LLMs has not been explored in detail. In this work, we present a Monte Carlo Tree Search-based approach that improves beyond state-of-the-art chain-of-thought prompting variants to augment scientific reasoning. We introduce two new reasoning datasets: 1) a curation of computational chemistry simulations, and 2) diverse questions written by catalysis researchers for reasoning about novel chemical conversion processes. We improve over the best baseline by 25.8\% and find that our approach can augment scientist's reasoning and discovery process with novel insights.\footnote{All resources will be publicly available upon publication.
Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and multimodal parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, material structure image spaces, and molecular embedding spaces. Often these systems are black-boxes and time-consuming to evaluate, which resulted in strong interest towards active learning methods such as Bayesian optimization (BO). However, these systems are often noisy which make the black box function severely multi-modal and non-differentiable, where a vanilla BO can get overly focused near a single or faux optimum, deviating from the broader goal of scientific discovery. To address these limitations, here we developed Strategic Autonomous Non-Smooth Exploration (SANE) to facilitate an intelligent Bayesian optimized navigation with a proposed cost-driven probabilistic acquisition function to find multiple global and local optimal regions, avoiding the tendency to becoming trapped in a single optimum. To distinguish between a true and false optimal region due to noisy experimental measurements, a human (domain) knowledge driven dynamic surrogate gate is integrated with SANE. We implemented the gate-SANE into pre-acquired piezoresponse spectroscopy data of a ferroelectric combinatorial library with high noise levels in specific regions, and piezoresponse force microscopy (PFM) hyperspectral data. SANE demonstrated better performance than classical BO to facilitate the exploration of multiple optimal regions and thereby prioritized learning with higher coverage of scientific values in autonomous experiments. Our work showcases the potential application of this method to real-world experiments, where such combined strategic and human intervening approaches can be critical to unlocking new discoveries in autonomous research.
The evaluation of constitutive models, especially for high-risk and high-regret engineering applications, requires efficient and rigorous third-party calibration, validation and falsification. While there are numerous efforts to develop paradigms and standard procedures to validate models, difficulties may arise due to the sequential, manual, and often biased nature of the commonly adopted calibration and validation processes, thus slowing down data collections, hampering the progress towards discovering new physics, increasing expenses and possibly leading to misinterpretations of the credibility and application ranges of proposed models. This work attempts to introduce concepts from game theory and machine learning techniques to overcome many of these existing difficulties. Here, we introduce an automated meta-modeling game where two competing AI agents systematically generate experimental data to calibrate a given constitutive model and to explore its weakness such that the experiment design and model robustness can be improved through competitions. The two agents automatically search for the Nash equilibrium of the meta-modeling game in an adversarial reinforcement learning framework without human intervention. In particular, a protagonist agent seeks to find the more effective ways to generate data for model calibrations, while an adversary agent tries to find the most devastating test scenarios that expose the weaknesses of the constitutive model calibrated by the protagonist. By capturing all possible design options of the laboratory experiments into a single decision tree, we recast the design of experiments as a game of combinatorial moves that can be resolved through deep reinforcement learning by the two competing players. Our adversarial framework emulates idealized scientific collaborations and competitions among researchers to achieve a better understanding of the application range of the learned material laws and prevent misinterpretations caused by conventional AI-based third-party validation. Numerical examples are given to demonstrate the wide applicability of the proposed meta-modeling game with adversarial attacks on both human-crafted constitutive models and machine learning models.
Recently, a new graph Laplacian, called the inner product Laplacian, was introduced which generalizes many existing Laplacians, including the normalized and combinatorial Laplacian and their weighted variants. The key observation behind the inner product Laplacian is that by defining appropriate inner product spaces on the vertices and edges, the standard Laplacians can be recovered as Hodge Laplacians over the simplicial complex formed by the edges and vertices. These inner product spaces form a natural way to incorporate non-combinatorial information into the definition of a domain-specific Laplacian. In particular, in contrast to current domain-specific weighting schemes which rely solely on edge weights, information regarding the similarity of non-adjacent vertices and arbitrary pairs of edges can be effectively incorporated into the Laplacian. In order to illustrate this approach we consider the problem of calculating the potential energy of an atomistic configuration using Graph Neural Networks. In comparison with start-of-the-art approaches, such as SchNet, our approach replaces a learned (via auto-encoder) representation of the atom types with an inner product space on atoms based on scientific knowledge (e.g., electronegativity). We will illustrate how this approach captures key chemical properties of the molecules and compare the energy calculations with state-of-the-art neural network approaches. However, to compute the resulting Laplacian involves a mixture of sparse and dense matrix computation and yields a dense matrix as the basis for the graph convolution. This dense convolutional kernel necessitates moving away from the standard message passing framework for graph neural networks and increases the computational cost of applying the kernel. In order to mitigate these costs we investigate means of leveraging the mixed sparse and dense computations to reduce the overall computational cost and how these approaches can be automatically transferred to energy efficient hardware (e.g., field programmable gate arrays (FPGAs)).
As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2
As the growing availability of computational power slows, there has been an increasing reliance on algorithmic advances. However, faster algorithms alone will not necessarily bridge the gap in allowing computational scientists to study problems at the edge of scientific discovery in the next several decades. Often, it is necessary to simplify or precondition solvers to accelerate the study of large systems of linear equations commonly seen in a number of scientific fields. Preconditioning a problem to increase efficiency is often seen as the best approach; yet, preconditioners which are fast, smart, and efficient do not always exist. Following the progress of [1], we present a new preconditioner for symmetric diagonally dominant (SDD) systems of linear equations. These systems are common in certain PDEs, network science, and supervised learning among others. Based on spectral support graph theory, this new preconditioner builds off of the work of [2], computing and applying a V-cycle chain of approximate inverse matrices. This preconditioner approach is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved. Due to its generation of an Approximate Inverse Chain of matrices, we refer to this as the AIC preconditioner. We further accelerate the AIC preconditioner by utilizing precomputations to simplify setup and multiplications in the con-text of an iterative Krylov-subspace solver. While these iterative solvers can greatly reduce solution time, the number of iterations can grow large quickly in the absence of good preconditioners. Initial results for the AIC preconditioner have shown a very large reduction in iteration counts for SDD systems as compared to standard preconditioners such as Incomplete Cholesky (ICC) and Multigrid (MG). We further show significant reduction in iteration counts against the more advanced Combinatorial Multigrid (CMG) preconditioner. We have further developed no-fill sparsification techniques to ensure that the computational cost of applying the AIC preconditioner does not grow prohibitively large as the depth of the V-cycle grows for systems with larger condition numbers. Our numerical results have shown that these sparsifiers maintain the sparsity structure of our system while also displaying significant reductions in iteration counts.1 2
The overarching goal of this project is to understand the phase stability and mechanical behavior of non-stoichiometric multi-principal element alloy (MPEA) materials. In order to identify suitable alloys, we plan to use a combinatorial thin film screening approach, in collaboration with scientists at Lawrence Berkeley National Laboratory who are performing computational work as well as complementary experimental work. Specific tasks within the scope of this project include the fabrication, using thin film deposition from six sputtering targets, of combinatorial samples with multi-dimensional gradients in composition and microstructure. These samples are studied to screen MPEA systems for promising candidate alloys with specific composition(s), based on characterization of composition, structure and mechanical behavior across the thin film. We want to produce single-phase MPEAs with chemical homogeneity in a given thin film region, simple grain structures, and no intermetallic phases present. Gradient films facilitate first-pass screening for desirable characteristics and inform the next stage of work that involves fabrication of bulk MPEA specimens for (tensile) mechanical testing and characterization. To make the bulk alloys, metal (elemental) pieces are melted to form MPEAs, followed by heat treatment to homogenize the composition and microstructure. A subset of alloys is also cast, using vacuum arc melting, to yield larger samples (diameter ~1 cm and length ~5-10 cm) and these allow us to assess viability of scale-up for the alloys in structural applications. Further processing plans include rolling and heat treatment to recrystallize selected bulk MPEAs and grow grains to different extents, in order to investigate size effects in the mechanical behavior of MPEAs. Microspecimen testing will be performed (primarily in tension) to assess the mechanical behavior over a range of temperatures. The deformation microstructure of mechanically tested alloys will be characterized using transmission electron microscopy (TEM) to provide a scientific basis for understanding the structure-property relationships in MPEA mechanical behavior.