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DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Cutting the Deployment Costs of Physics-Based MPC in Buildings by Simulation-Based Imitation Learning

It has been shown that model predictive control (MPC) is a promising solution for energy-efficient building operations. However, the deployment of MPC in a large portion of the building stock has not been possible partially because of high installation costs. Every building is unique and requires a tailored MPC solution. The best performing solutions are often based on physics-based modeling, which is, however, computationally expensive and requires dedicated software. A promising direction that tackles this problem is to train a neural network-based optimal control policy to imitate the behavior of physics-based MPC from the simulation data generated offline. The neural networks give control actions that closely approximate those produced by physics-based MPC, but with a fraction of the computational and memory requirements and without the need for licensed software. The main advantage of the proposed approach stems from simple evaluation at execution time, leading to low computational footprints and easy deployment on embedded HW platforms. In the case study, we present the energy savings potential of physics-based MPC applied to an office building in Belgium. We demonstrate how neural network approximators can be used to cut the implementation and maintenance costs of MPC deployment without compromising performance. We also critically assess the presented approach by pointing out the remaining challenges and open research questions.

Drgona, Jan↗

DOE OSTI2025

Optimizing the design and operation of water networks: Two decomposition approaches

We consider the design and operation of water networks simultaneously. Water network problems can be divided into two categories: the design problem and the operation problem. The design problem involves determining the appropriate pipe sizing and placements of pump stations, while the operation problem involves scheduling pump stations over multiple time periods to account for changes in supply and demand. Our focus is on networks that involve water co-produced with oil and gas. While solving the optimization formulation for such networks, we found that obtaining a primal (feasible) solution is more challenging than obtaining dual bounds using off-the-shelf mixed-integer nonlinear programming solvers. Therefore, we propose two methods to obtain good primal solutions. One method involves a decomposition framework that utilizes a convex reformulation, while the other is based on time decomposition. To test our proposed methods, we conduct computational experiments on a network derived from the PARETO case study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Reinforcement Learning for Distribution Grid Optimization (PyCIGAR) v0.1

PyCIGAR is a python software package that merges off-the-shelf reinforcement learning libraries (RLLib and Ray) with electric power distribution system simulation tools (OpenDSS and a custom power flow solver built by LBL). PyCIGAR enables the training of neural networks to optimize the behavior of different components in the electric distribution grid, such as control systems in photovoltaic rooftop solar inverters and electric battery storage systems. The software package has been used to train neural networks to update settings in photovoltaic rooftop solar inverter control systems to mitigate cyber attacks on other solar photovoltaic rooftop devices.

Arnold, Daniel↗

DOE OSTI2022

Mobility Energy Productivity Evaluation of Prediction-Based Vehicle Powertrain Control Combined with Optimal Traffic Management

Transportation vehicle and network system efficiency can be defined in two ways: 1) reduction of travel times across all the vehicles in the system, and 2) reduction in total energy consumed by all the vehicles in the system. The mechanisms to realize these efficiencies are treated as independent (i.e., vehicle and network domains) and, when combined, they have not been adequately studied to date. This research aims to integrate previously developed and published research on Predictive Optimal Energy Management Strategies (POEMS) and Intelligent Traffic Systems (ITS), to address the need for quantifying improvement in system efficiency resulting from simultaneous vehicle and network optimization. POEMS and ITS are partially independent methods which do not require each other to function but whose individual effectiveness may be affected by the presence of the other. In order to evaluate the system level efficiency improvements, the Mobility Energy Productivity (MEP) metric is used. MEP specifically measures the connectedness of a system while accounting for time and energy externalities of modes that provide mobility in a given location. A SUMO model is developed to reflect real traffic patterns in Fort Collins, Colorado and data is collected by a probe SUMO vehicle which is validated against data collected on a real vehicle driving the same routes through the city. Individual vehicle and system level efficiencies are calculated using SUMO outputs for scenarios which integrate POEMS and ITS independently as well as jointly. Results from application of POEMS and ITS show improvement in energy consumption and travel times respectively when compared to the respective baseline scenarios. Our conclusion is that there are promising synergistic benefits to travel time and energy efficiency when POEMS and ITS are combined.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2026

Plan It Together: Optimizing Across Generation, Transmission, Distribution, and Distributed Energy Resources

Integrated planning holds the promise of unlocking lower total system cost solutions by connecting previously siloed planning processes. This article summarizes the state of bulk and local grid planning today and details multiple new analytical approaches that can enable more holistic planning methods to develop comprehensive solutions to generation, transmission, distribution, and distributed energy resource needs. These include both iterative approaches as well as cooptimization techniques. In addition to the benefits of these methods, the technical and institutional challenges and associated solutions are also discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Scalable deep learning for watershed model calibration

Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters often need to be estimated/calibrated through inverse modeling to produce reliable predictions on hydrological fluxes and states. Existing parameter estimation methods can be time consuming, inefficient, and computationally expensive for high-dimensional problems. In this paper, we present an accurate and robust method to calibrate the SWAT model (i.e., 20 parameters) using scalable deep learning (DL). We developed inverse models based on convolutional neural networks (CNN) to assimilate observed streamflow data and estimate the SWAT model parameters. Scalable hyperparameter tuning is performed using high-performance computing resources to identify the top 50 optimal neural network architectures. We used ensemble SWAT simulations to train, validate, and test the CNN models. We estimated the parameters of the SWAT model using observed streamflow data and assessed the impact of measurement errors on SWAT model calibration. We tested and validated the proposed scalable DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the CNN-based calibration is better than two popular parameter estimation methods (i.e., the generalized likelihood uncertainty estimation [GLUE] and the dynamically dimensioned search [DDS], which is a global optimization algorithm). For the set of parameters that are sensitive to the observations, our proposed method yields narrower ranges than the GLUE method but broader ranges than values produced using the DDS method within the sampling range even under high relative observational errors. The SWAT model calibration performance using the CNNs, GLUE, and DDS methods are compared using R 2 and a set of efficiency metrics, including Nash-Sutcliffe, logarithmic Nash-Sutcliffe, Kling-Gupta, modified Kling-Gupta, and non-parametric Kling-Gupta scores, computed on the observed and simulated watershed responses. The best CNN-based calibrated set has scores of 0.71, 0.75, 0.85, 0.85, 0.86, and 0.91. The best DDS-based calibrated set has scores of 0.62, 0.69, 0.8, 0.77, 0.79, and 0.82. The best GLUE-based calibrated set has scores of 0.56, 0.58, 0.71, 0.7, 0.71, and 0.8. The scores above show that the CNN-based calibration leads to more accurate low and high streamflow predictions than the GLUE and DDS sets. Our research demonstrates that the proposed method has high potential to improve our current practice in calibrating large-scale integrated hydrologic models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Tuning successive linear programming to solve AC optimal power flow problem for large networks

Successive linear programming (SLP) is a practical approach for solving large-scale nonlinear optimization problems. Alternating current optimal power flow (ACOPF) is no exception, particularly the large size of real-world networks. However, in order to achieve tractability, it is essential to tune the SLP algorithm presented in the literature. This paper presents a modified SLP algorithm to solve the ACOPF problem, specified by the U.S. Department of Energy’s (DOE) Grid Optimization (GO) Competition Challenge 1, within strict time limits. The algorithm first finds a near-optimal solution for the relaxed problem (i.e., Stage 1). Then, it finds a feasible solution in the proximity of the near-optimal solution (i.e., Stage 2 and Stage 3). The numerical experiments on test cases ranging from 500-bus to 30,000-bus systems show that the algorithm is tractable. Here the results show that our proposed algorithm is tractable and can solve more than 80% of test cases faster than the well-known Interior Point Method while significantly reduce the number of iterations required to solve ACOPF. The number of iterations is considered an important factor in the examination of tractability which can drastically reduce the computational time required within each iteration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Pipeline Hydrogen Decarbonization and Repurposing Analyzers (P-HyDRAs)

The Pipeline Hydrogen Decarbonization and Repurposing Analyzers (P-HyDRAs) are a set of prototype computational tools for simulating and optimizing midstream natural gas pipeline system operations subject to location and time-dependent hydrogen blending. The models can accurately resolve dynamic gas flows through large-scale pipeline networks using non-ideal gas equations of state. The codes can be used as decision support for planning and design decisions involving intra-day energy flow schedules as well as spatiotemporal economic values of natural gas, hydrogen, and net energy delivered to consumers while ensuring that pipeline hydraulic limitations, gas compressor station constraints, operational factors, and pre-existing shipping contracts are satisfied. The inputs to the codes are a model of the pipeline system as well as time-series data that specify boundary conditions on the network. For optimization, the code module requires price and quantity offers for natural gas and hydrogen and price and quantity bids for energy, which are used as time-dependent constraints in an optimal control problem. The outputs are time-series data that provide a predictive simulation of gas flows, mass fractions, and pressures, or with additional degrees of freedom give an approximately optimal solution for gas injections/withdrawals, compressor settings, and sensitivities to the objective function that provide locational values of energy.

Zlotnik, Anatoly↗

DOE OSTI2024

Complexity-calibrated benchmarks for machine learning reveal when prediction algorithms succeed and mislead

Abstract Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a “next-generation” reservoir computer was introduced in which the memory trace involves only a finite number of previous symbols. We explore the inherent limitations of finite-past memory traces in this intriguing proposal. A lower bound from Fano’s inequality shows that, on highly non-Markovian processes generated by large probabilistic state machines, next-generation reservoir computers with reasonably long memory traces have an error probability that is at least $$\sim 60\%$$ ∼ 60 % higher than the minimal attainable error probability in predicting the next observation. More generally, it appears that popular recurrent neural networks fall far short of optimally predicting such complex processes. These results highlight the need for a new generation of optimized recurrent neural network architectures. Alongside this finding, we present concentration-of-measure results for randomly-generated but complex processes. One conclusion is that large probabilistic state machines—specifically, large $$\epsilon$$ ϵ -machines—are key to generating challenging and structurally-unbiased stimuli for ground-truthing recurrent neural network architectures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Deep Learning At Depth: Estimating subsurface parameters from geophysical monitoring data

Geophysical imaging techniques are a non-invasive way to image the subsurface and understand both subsurface solid (rock/soil) and fluid property distributions and their evolution in time. Inversions of the geophysical data, such as Electrical Resistance Tomography (ERT) data, are solved to estimate the subsurface property distributions, such as conductivity, and many inversion techniques smooth out sharp gradients in rock or fluid property distributions. Sharp gradients in subsurface properties tend to be present in situations with complex subsurface structures, which are common in many subsurface applications. We have successfully demonstrated that it is possible to inform, or constrain, inversions with neural networks trained on synthetic data with complex subsurface structures. Initial results suggest this process may be optimizable to yield property distributions that better represent the true property distributions than the same inversion process without the neural network constraint. Future work would optimize the neural network performance for this application and then apply the synthetic-data trained neural network to real data to understand the utility and performance of this technique for real data sets.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Finding Your Niche: An Evolutionary Approach to HPC Topologies

Traditional interconnection network design approaches focus on building general network topologies by optimizing the bisection bandwidth or minimizing the network’s diameter to reduce the maximum distance between any two nodes, thus amortizing the overall execution time of the HPC workloads. While such network topologies may accommodate a wide variety of applications in general, this may result in sub-optimal performance for many frequently-executed or dynamic workloads. In this paper, instead of focusing on designing an all-encompassing, general-purpose network topology, we develop a methodology to design customized network interconnects, evolved by “finding” the optimal topologies for a particular target workload given by its communication and contention profiles. To this end, we implement a Genetic Algorithm (GA)-based approach for network topology design tailored to improve the overall execution time of a particular workload of interest. We conducted extensive experiments with well-known motifs in physics-based workloads (Sweep3D and FFT), as well as with a representative graph application (MiniVite), using the well-known Structural Simulation Toolkit (SST) Macroscale Element Library (SST/macro) simulator for network interconnect evaluation. We demonstrate that our genetic algorithm-based approach is robust enough to find the underlying optimal topology of a particular workload.

network interconnects, graph search, meta-heuristi↗

DOE OSTI2020

Evaluation of Graph Analytics Frameworks Using the GAP Benchmark Suite

The analysis of connected data is an increasingly important application in high-performance computing. Such analyses can reveal fraudulent patterns in financial transactions, optimize telecommunications networks, predict information flow in social networks, etc. However, the landscape of graph analytics is highly diverse. Graph algorithms stress processor architectures differently, and no one graph can represent all topologies. Consequently, no single approach or framework is expected to be optimal for all graph analytics problems. To help make sense of this diverse landscape, we evaluated four approaches to graph analytics: GraphBLAS, Galois, BGL17, GraphIt; and compare them against hand-tuned implementations that take advantage of hardware features on our test platform. Graph- BLAS formulates graph analytics as sparse linear algebra. Galois provides syntactic constructs for data parallelism over irregular data structures. BGL17 is a generic C++ template library for implementing graph algorithms. GraphIt provides a domain- specific language to describe and optimize graph algorithms. We use the GAP Benchmark Suite to establish baseline performance and guide the side-by-side evaluation of each framework. GAP consists of 30 tests: six graph analytics algorithms (breadth- first search, single-source shortest path, PageRank, betweenness centrality, connected components, and triangle counting) run on five graphs, each with different topological characteristics (e.g., high diameter, skewed degree distribution, high average degree). High-performance reference implementations are included for each benchmark algorithm. Because a graph can be loaded into memory a number of ways (e.g., flat file on disk, compressed sparse format, data frames, retrieved from SQL or NoSQL databases), our evaluation focused on computational performance rather than I/O. Our results show the relative strengths of each framework.

Graph algorithms, Benchmarking, shared-memory prog↗

DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗

DOE OSTI2022

Shape memory polymers

New shape memory polymer compositions, methods for synthesizing new shape memory polymers, and apparatus comprising an actuator and a shape memory polymer wherein the shape memory polymer comprises at least a portion of the actuator. A shape memory polymer comprising a polymer composition which physically forms a network structure wherein the polymer composition has shape-memory behavior and can be formed into a permanent primary shape, re-formed into a stable secondary shape, and controllably actuated to recover the permanent primary shape. Polymers have optimal aliphatic network structures due to minimization of dangling chains by using monomers that are symmetrical and that have matching amine and hydroxl groups providing polymers and polymer foams with clarity, tight (narrow temperature range) single transitions, and high shape recovery and recovery force that are especially useful for implanting in the human body.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Shape memory polymers

Wilson, Thomas S.↗

DOE OSTI2022

Open-source FPGA-ML codesign for the MLPerf Tiny Benchmark

We present our development experience and recent results for the MLPerf Tiny Inference Benchmark on field-programmable gate array (FPGA) platforms. We use the open-source hls4ml and FINN workflows, which aim to democratize AI-hardware codesign of optimized neural networks on FPGAs. We present the design and implementation process for the keyword spotting, anomaly detection, and image classification benchmark tasks. The resulting hardware implementations are quantized, configurable, spatial dataflow architectures tailored for speed and efficiency and introduce new generic optimizations and common workflows developed as a part of this work. The full workflow is presented from quantization-aware training to FPGA implementation. The solutions are deployed on system-on-chip (Pynq-Z2) and pure FPGA (Arty A7-100T) platforms. The resulting submissions achieve latencies as low as 20 $\mu$s and energy consumption as low as 30 $\mu$J per inference. We demonstrate how emerging ML benchmarks on heterogeneous hardware platforms can catalyze collaboration and the development of new techniques and more accessible tools.

Borras, Hendrik↗