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DOE OSTI2022

Deep transfer operator learning for partial differential equations under conditional shift

Transfer learning enables the transfer of knowledge gained while learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labelling, potential computational power limitations and dataset distribution mismatches. Here, we propose a new transfer learning framework for task-specific learning (functional regression in partial differential equations) under conditional shift based on the deep operator network (DeepONet). Task-specific operator learning is accomplished by fine-tuning task-specific layers of the target DeepONet using a hybrid loss function that allows for the matching of individual target samples while also preserving the global properties of the conditional distribution of the target data. Inspired by conditional embedding operator theory, we minimize the statistical distance between labelled target data and the surrogate prediction on unlabelled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various transfer learning scenarios involving nonlinear partial differential equations under diverse conditions due to shifts in the geometric domain and model dynamics. Our transfer learning framework enables fast and efficient learning of heterogeneous tasks despite considerable differences between the source and target domains.

42 ENGINEERING↗

DOE OSTI2021

Solar Transposition Modeling via Deep Neural Networks With Sky Images

This article presents a notable advance toward the development of a new method of increasing the single-axis tracking photovoltaic (PV) system power output by improving the determination and near-term prediction of the optimum module tilt angle. The tilt angle of the plane receiving the greatest total irradiance changes with Sun position and atmospheric conditions including cloud formation and movement, aerosols, and particulate loading, as well as varying albedo within a module's field of view. In this article, we present a multi-input convolutional neural network that can create a profile of plane-of-array irradiance versus surface tilt angle over a full 180° arc from horizon to horizon. As input, the neural network uses the calculated solar position and clear-sky irradiance values, along with sky images. The target irradiance values are provided by the multiplanar irradiance sensor (MPIS). In order to account for varying irradiance conditions, the MPIS signal is normalized by the theoretical clear-sky global horizontal irradiance. Using this information, the neural network outputs an N -dimensional vector, where N is the number of points to approximate the MPIS curve via Fourier resampling. The output vector of the model is smoothed with a Gaussian kernel to account for error in the downsamping and subsequent upsampling steps, as well as to smooth the unconstrained output of the model. Furthermore, these profiles may be used to perform near-term prediction of angular irradiance, which can then inform the movement of a PV tracker.

42 ENGINEERING↗

DOE OSTI2023

Towards On-Chip Learning for Low Latency Reasoning with End-to-End Synthesis

The Software Defined Architectures (SODA) Synthesizer is an open-source compiler-based tool able to automatically generate domain-specialized systems targeting Application-Specific Integrated Circuits (ASICs) or Field Programmable Gate Arrays (FPGAs) starting from high-level programming. SODA is composed of a frontend, SODA-OPT, which leverages the multilevel intermediate representation (MLIR) framework to interface with productive programming tools (e.g., machine learning frame-works), identify kernels suitable for acceleration, and perform high-level optimizations, and of a state-of-the-art high-level synthesis backend, Bambu from the PandA framework, to generate custom accelerators. One specific application of the SODA Synthesizer is the generation of accelerators to enable ultra-low latency inference and control on autonomous systems for scientific discovery (e.g., electron microscopes, sensors in particle accelerators, etc.). This paper provides an overview of the flow in the context of the generation of accelerators for edge processing to be integrated in transmission electron microscopy (TEM) devices, focusing on use cases from precision material synthesis. We show the tool in action with an example of design space exploration for inference on reconfigurable devices with a conventional deep neural network model (LeNet). Finally, we discuss the research directions and opportunities enabled by SODA in the area of autonomous control for scientific experimental workflows.

Castellana, Vito G.↗

DOE OSTI2024

RAP: Resource-aware Automated GPU Sharing for Multi-GPU Recommendation Model Training and Input Preprocessing

Ensuring high-quality recommendations for newly onboarded users requires the continuous retraining of Deep Learning Recommendation Models (DLRMs) with freshly generated data. To serve the online DLRM retraining, existing solutions use hundreds of CPU computing nodes designated for input preprocessing, causing significant power consumption that surpasses even the power usage of GPU trainers. To this end, we propose RAP, an end-to-end DLRM training framework that supports Resource-aware Automated GPU sharing for DLRM input Preprocessing and Training. The core idea of RAP is to accurately capture the remaining GPU computing resources during DLRM training for input preprocessing, achieving superior training efficiency without requiring additional resources. Specifically, RAP utilizes a co-running cost model to efficiently assess the costs of various input preprocessing operations, and it implements a resource-aware horizontal fusion technique that adaptively merges smaller kernels according to GPU availability, circumventing any interference with DLRM training. In addition, RAP leverages a heuristic searching algorithm that jointly optimizes both the input preprocessing graph mapping and the co-running schedule to maximize the end-to-end DLRM training throughput. The comprehensive evaluation shows that RAP achieves 78.3× speedup on average over CPU-based DLRM input preprocessing frameworks. In addition, the end-to-end training throughput of RAP is only 2.04% lower than the ideal case, which has no input preprocessing overhead.

Wang, Zheng↗

DOE OSTI2023

Digital Modeling on Large Kernel Metamaterial Neural Network

Deep neural networks (DNNs) utilized recently are physically deployed with computational units (e.g., CPUs and GPUs). Such a design might lead to a heavy computational burden, significant latency, and intensive power consumption, which are critical limitations in applications such as Internet of Things (IoT), edge computing, and usage of drones. Recent advances in optical computational units (e.g., metamaterial) have shed light on energy-free and light-speed neural networks. However, the digital design of the metamaterial neural network (MNN) is fundamentally limited by its physical limitations, such as precision, noise, and bandwidth during fabrication. Moreover, the unique advantages of MNN’s (e.g., light-speed computation) are not fully explored via standard 3×3 convolution kernels. In this paper, we propose a novel large kernel metamaterial neural network (LMNN) that maximizes the digital capacity of the state-of-the-art (SOTA) MNN with model re-parametrization and network compression, while also considering the optical limitation explicitly. The new digital learning scheme can maximize the learning capacity of MNN while modeling the physical restrictions of meta-optics. With the proposed LMNN, the computation cost of the convolutional front-end can be offloaded to fabricated optical hardware. The experimental results on two publicly available datasets demonstrate that the optimized hybrid design improved classification accuracy while reducing computational latency. In conclusion, the development of the proposed LMNN is a promising step towards the ultimate goal of energy-free and light-speed AI.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Software-Hardware Co-design of Heterogeneous SmartNIC System for Recommendation Models Inference and Training

Deep Learning Recommendation Models (DLRMs) are critical applications in various domains and have evolved as one of the single largest machine learning applications. Trillions of DLRM parameters exceed the on-chip memory capacity of GPUs. Large-scale multi-node systems are required for distributed DLRM inference and training, which suffer from the all-to-all communication bottleneck, mainly limiting the scalability of ever-growing DLRMs. In recent years, SmartNICs have evolved with coupled computation and communication capabilities providing opportunities for a powerful heterogeneous device in the system. However, there isn't such a distributed system that fully leverages the abundant smartNIC resources that resolve the scalability issue of DLRMs. In this work, we proposed a software-hardware co-design of a heterogeneous smartNIC system that resolves the communication bottleneck of distributed DLRMs, mitigates the memory bandwidth pressure, and improves computation efficiency. We provide a set of smartNIC designs of cache systems (including local cache and remote cache) and smartNIC computation kernels which reduce data movement, relieve memory lookup intensity, and improve the GPU's computation efficiency. In addition, we propose a graph algorithm that improves the data locality of queries within batches which optimizes the overall system performance with higher data reuse. Our evaluation shows that our system achieves 2.1x latency speedup for inference and 1.6x throughput speedup for training.

Guo, Anqi↗

DOE OSTI2024

Scalable Risk Assessment of Rare Events in Power Systems With Uncertain Wind Generation and Loads

Risk assessment of rare events has become increasingly important in power system planning and operation with the increasing integration of renewable energy and the presence of system uncertainties. However, quantifying the risk posed by rare events via the traditional method, i.e., Monte Carlo sampling (MCS), incurs substantial computational expense stemming from the vast ensemble of power flow simulations. To accelerate the assessment, this paper proposes a Deep Neural Network (DNN)-kernelized vector-valued Gaussian Process (VVGP) approach with excellent computational efficiency while maintaining high accuracy. Consequently, serving as a surrogate model for the power flow solver, the DNN-kernelized VVGP enables significantly faster but accurate risk assessment compared to the power flow solver. The developed surrogate model evaluates low-order N - k events that contain more than 90% instances by adeptly capturing the topological features while the high-order N - k events are assessed via a power flow solver, thereby striking a balance between computational efficiency and uncertainty quantification accuracy. Moreover, the model incorporates a Support Vector Machine (SVM) classifier to resample concerning low-probability tail events to counteract the biases potentially introduced during the DNN-kernelized VVGP evaluations. Simulations conducted on the modified IEEE 24-bus, 118-bus, and European 1354-bus systems demonstrate that the proposed method maintains the accuracy benchmark set by MCS while significantly reducing computational demands in large-scale power systems as compared to other state-of-the-art methods.

17 WIND ENERGY↗

DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

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