Divide-and-conquer the NAS puzzle in resource-constrained federated learning systems
Not provided.
Computer Science↗
SEARCH · Search NASA
Results for “divide-and-conquer”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian
We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024
Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗
Quantum Circuit Cutting for Classical Shadows
Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits and discuss the mechanisms for this advantage.
97 MATHEMATICS AND COMPUTING↗
On the Training and Generalization of Deep Operator Networks
Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.
deep operator networks↗
Effects of pH on an IDP conformational ensemble explored by molecular dynamics simulation
The conformational ensemble of intrinsically disordered proteins, such as α-synuclein, are responsible for their function and malfunction. Misfolding of α-synuclein can lead to neurodegenerative diseases, and the ability to study their conformations and those of other intrinsically disordered proteins under varying physiological conditions can be crucial to understanding and preventing pathologies. In contrast to well-folded peptides, a consensus feature of IDPs is their low hydropathy and high charge, which makes their conformations sensitive to pH perturbation. We examine a prominent member of this subset of IDPs, α-synuclein, using a divide-and-conquer scheme that provides enhanced sampling of IDP structural ensembles. We constructed conformational ensembles of α-synuclein under neutral (pH ~ 7) and low (pH ~ 3) pH conditions and compared our results with available information obtained from smFRET, SAXS, and NMR studies. Specifically, α-synuclein has been found to in a more compact state at low pH conditions and the structural changes observed are consistent with those from experiments. We also characterize the conformational and dynamic differences between these ensembles and discussed the implication on promoting pathogenic fibril formation. We find that under low pH conditions, neutralization of negatively charged residues leads to compaction of the C-terminal portion of α-synuclein while internal reorganization allows α-synuclein to maintain its overall end-to-end distance. Here, we also observe different levels of intra-protein interaction between three regions of α-synuclein at varying pH and a shift towards more hydrophilic interactions with decreasing pH.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Projector-Free Capped-Fragment Scheme within Density Functional Embedding Theory for Covalent and Ionic Compounds
Quantum-mechanics-(QM)-based simulations now routinely aid in understanding and even discovering new chemistries involving molecules and materials exhibiting desired functionalities. Ab initio correlated wavefunction (CW) theories systematically improve QM methods, with many exhibiting high accuracy. However, execution of CW methods requires expensive computations that typically scale poorly with system size. Divide-and-conquer approaches partition large systems into smaller fragments; a lower level of theory treats fragment interactions while a preferred higher level of theory describes the important fragment. These methods offer ways to incorporate CWs into chemical simulations of large systems, e.g., biomolecules, surfaces, large inorganic clusters, bulk crystals, etc. Here we propose a partitioning protocol that utilizes capping atoms to saturate severed covalent bonds at fragment interfaces and density functional embedding theory (DFET) to describe fragment interactions. The capping groups in each fragment provide an ad-hoc potential that approximates the effects of the environment. An embedding potential optimized via DFET then serves as an augmentation of the capping group to simulate the effects of the environment. We concurrently use an auxiliary fragment (a separate system comprised of only the combined capping groups) to account for, and thereby correct, the electron density contributions of all the capping groups added to all of the fragments. This method depends only on the capped-subsystem and auxiliary-fragment electron densities, forgoing, as with the original DFET developed for metallic systems, orbital-based projector approaches that determine a nonlocal action of the embedding potential onto the fragment electrons. By using an auxiliary fragment, the method maintains a purely electron-density-dependent embedding potential, substantially lessening the cost and leading to simpler implementation. In this work, we demonstrate the utility of our capped-DFET and ensuing capped embedded CW method in two contrasting systems, namely, an organic molecule and an ionic metal oxide cluster.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Heterologous synthesis of the complex homometallic cores of nitrogenase P- and M-clusters in Escherichia coli
Nitrogenase is an active target of heterologous expression because of its importance for areas related to agronomy, energy, and environment. One major hurdle for expressing an active Mo-nitrogenase in Escherichia coli is to generate the complex metalloclusters (P- and M-clusters) within this enzyme, which involves some highly unique bioinorganic chemistry/metalloenzyme biochemistry that is not generally dealt with in the heterologous expression of proteins via synthetic biology; in particular, the heterologous synthesis of the homometallic P-cluster ([Fe 8 S 7 ]) and M-cluster core (or L-cluster; [Fe 8 S 9 C]) on their respective protein scaffolds, which represents two crucial checkpoints along the biosynthetic pathway of a complete nitrogenase, has yet to be demonstrated by biochemical and spectroscopic analyses of purified metalloproteins. Here, we report the heterologous formation of a P-cluster-containing NifDK protein upon coexpression of Azotobacter vinelandii nifD, nifK, nifH, nifM, and nifZ genes, and that of an L-cluster-containing NifB protein upon coexpression of Methanosarcina acetivorans nifB, nifS, and nifU genes alongside the A. vinelandii fdxN gene, in E. coli. Our metal content, activity, EPR, and XAS/EXAFS data provide conclusive evidence for the successful synthesis of P- and L-clusters in a nondiazotrophic host, thereby highlighting the effectiveness of our metallocentric, divide-and-conquer approach that individually tackles the key events of nitrogenase biosynthesis prior to piecing them together into a complete pathway for the heterologous expression of nitrogenase. As such, this work paves the way for the transgenic expression of an active nitrogenase while providing an effective tool for further tackling the biosynthetic mechanism of this important metalloenzyme.
59 BASIC BIOLOGICAL SCIENCES↗
Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling
Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. Here, in this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N-qubit local Hamiltonian. After a total evolution time of $\mathscr{O}$(ε –1 ), the proposed algorithm can efficiently estimate any parameter in the N-qubit Hamiltonian to ε error with high probability. Our algorithm uses ideas from quantum simulation to decouple the unknown N-qubit Hamiltonian H into noninteracting patches and learns H using a quantum-enhanced divide-and-conquer approach. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses polylog(ε –1 ) experiments. In contrast, the best existing algorithms require $\mathscr{O}$(ε –2 ) experiments and total evolution time. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum Circuit Partitioning for Scalable Noise-Aware Quantum Circuit Re-Synthesis
Re-synthesis techniques are utilized to optimize the quantum circuit. To enable scalable re-synthesis a divide-and-conquer approach is adopted that partitions the circuit into smaller blocks, which are optimized independently. Several algorithms have been proposed to minimize the block number while maximizing the gate count of each block. However, they vary in their performance and may not yield the highest output fidelity. We propose a reinforcement learning-based quantum circuit partitioning framework that incorporates the physical properties of the quantum hardware to maximize the output fidelity post-quantum circuit optimization. To accelerate the training, we also propose a noise injection method that enables on-the-fly optimization in the reinforcement learning environment, independent of the adopted optimization/re-synthesis method at the block level. We evaluate our approach compared to different partitioning techniques using various quantum benchmarks executed on IBM Q Hanoi quantum computer.
Charrwi, Mohammad Walid↗
ChatHPC: Building the Foundations for a Productive and Trustworthy AI-Assisted HPC Ecosystem
ChatHPC democratizes large language models for the high-performance computing (HPC) community by providing the infrastructure, ecosystem, and knowledge needed to apply modern generative AI technologies to rapidly create specific capabilities for critical HPC components while using relatively modest computational resources. Our divide-and-conquer approach focuses on creating a collection of reliable, highly specialized, and optimized AI assistants for HPC based on the cost-effective and fast Code Llama fine-tuning processes and expert supervision. We target major components of the HPC software stack, including programming models, runtimes, I/O, tooling, and math libraries. Thanks to AI, ChatHPC provides a more productive HPC ecosystem by boosting important tasks related to portability, parallelization, optimization, scalability, and instrumentation, among others. With relatively small datasets (on the order of KB), the AI assistants, which are created in a few minutes by using one node with two NVIDIA H100 GPUs and the ChatHPC library, can create new capabilities with Meta’s 7-billion parameter Code Llama base model to produce high-quality software with a level of trustworthiness of up to 90% higher than the 1.8-trillion parameter OpenAI ChatGPT-4o model for critical programming tasks in the HPC software stack.
Young, Aaron [ORNL] (ORCID:0000000254484667)↗
EMMA: a new method for computing multiple sequence alignments given a constraint subset alignment
Abstract Background Adding sequences into an existing (possibly user-provided) alignment has multiple applications, including updating a large alignment with new data, adding sequences into a constraint alignment constructed using biological knowledge, or computing alignments in the presence of sequence length heterogeneity. Although this is a natural problem, only a few tools have been developed to use this information with high fidelity. Results We present EMMA (Extending Multiple alignments using MAFFT--add) for the problem of adding a set of unaligned sequences into a multiple sequence alignment (i.e., a constraint alignment). EMMA builds on MAFFT--add, which is also designed to add sequences into a given constraint alignment. EMMA improves on MAFFT--add methods by using a divide-and-conquer framework to scale its most accurate version, MAFFT-linsi--add, to constraint alignments with many sequences. We show that EMMA has an accuracy advantage over other techniques for adding sequences into alignments under many realistic conditions and can scale to large datasets with high accuracy (hundreds of thousands of sequences). EMMA is available at https://github.com/c5shen/EMMA . Conclusions EMMA is a new tool that provides high accuracy and scalability for adding sequences into an existing alignment.
Shen, Chengze↗
Inversion of downhole electrical measurements for proppant mapping using very fast simulated annealing
Proppant mapping is critical for optimizing fracture treatment design and improving wells’ productivity. An electrode-based resistivity tool concept was developed earlier for proppant mapping in cased-hole wells. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are performed by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded. The method relies on direct excitation of the casing, which is expected to overcome the severe limitations of induction tools in cased-hole wells. A forward model based on a finite volume method has been developed to simulate the tool’s response to one or multiple fractures. To enable the implementation of such a practical system in multistage fractured horizontal wells, a fast and robust inversion approach is required. To that end, we have developed a divide-and-conquer approach based on a global optimization algorithm very fast simulated annealing (VFSA). Specifically, the original inverse problem is divided into subproblems and each subproblem can be solved separately using VFSA. The results indicate that our approach can invert the data and output widths and radii of multiple fractures without requiring a large number of forward simulations. The robustness of the inverse solver is also tested by adding Gaussian noise to the synthetic data. We tested example cases that demonstrate that when up to 5% noise is introduced, VFSA still provides very accurate inversion results with moderate uncertainties. Inversion results with some more realistic conditions, e.g., tilted fractures, complex fractures, and so on, are also presented.
Geochemistry & Geophysics↗
Engineering Synthetic Anaerobic Consortia Inspired by the Rumen for Biomass Breakdown and Conversion
Lignocellulosic plant biomass is a widely-abundant renewable resource that can be harnessed for value-added production of fuels & chemicals. While microbes have been engineered to breakdown lignocellulose and turn released sugars into products, this remains an energy-intensive process that requires expensive pre-treatment and separation steps. Furthermore, it is difficult to engineer all desirable traits for breakdown and conversion into one organism. This project developed a new strategy that relies on microbial partnerships formed in the herbivore rumen to liberate sugars from crude plant biomass and convert that sugar to value-added chemicals. Microbial consortia consisting of fungi, bacteria, and archaea form tight associations in the herbivore rumen, which divide-and-conquer the difficult tasks of biomass breakdown. This project leveraged a “synthetic rumen” consortium composed of anaerobic fungi and chain-elongating bacteria to study which metabolites are shared and exchanged between microbes and identify strategies to bolster lignocellulose conversion to value-added products. Our approach developed high-throughput systems and synthetic biology approaches to realize stable synthetic consortia that route lignocellulosic carbon into short and medium chain fatty acids (SCFAs/MCFAs) rather than methane. Key research objectives were to (1) design and predict anaerobic fungal and bacterial consortia that efficiently convert lignocellulosic biomass into medium-chain fatty acids (MCFAs), (2) understand how fermentation parameters and microbe-microbe interactions regulate and drive microbiome metabolic fluxes, and (3) use genomic editing to alter the fermentation byproducts of anaerobic fungi and bolster MCFA titers and yields.
09 BIOMASS FUELS↗