These authors contributed equally to this work. Abstract Transfer learning (TL) enables the transfer of knowledge gained in learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labeling, potential computational power limitations, and dataset distribution mismatches. We propose a new TL framework for task-specific learning (functional regression in partial differential equations (PDEs)) 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 target data. Inspired by the conditional embedding operator theory, we minimize the statistical distance between labeled target data and the surrogate prediction on unlabeled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various TL scenarios involving nonlinear PDEs under diverse conditions due to shift in the geometric domain and model dynamics. TL framework enables fast and efficient learning of heterogeneous tasks despite significant differences between the source and target domains. Deep learning has been successfully employed to simulate computationally expensive complex physical processes described by partial differential equations (PDEs) and achieve superior performance that allows the acceleration of numerous tasks including uncertainty quantification (UQ), risk modeling and design optimization [1-6]. Despite this success, the predictive performance of such models is often limited by the availability of labeled data used for training. However, in many cases collecting large and sufficient labeled datasets can be computationally intractable (e.g., when high-fidelity or multiscale models are considered). Furthermore, learning in isolation, i.e., training a single predictive model for different but related tasks, can be extremely expensive. To tackle this bottleneck, knowledge between relevant domains can be leveraged in a framework known as transfer learning (TL) [7]. In this scenario, information from a model trained on a specific domain (source) with sufficient labeled data can be transferred to a different but closely related domain (target) for which only a small number of training data is available.

We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whose discrete Laplace operator converges to the Laplace--Beltrami operator. We derive first order optimal potentials for the problem under consideration and find that the resulting solutions exhibit a surprising resemblance to the well-known Barenblatt--Prattle solution of the porous medium equation. Then, relying on these first order optimal potentials, we derive the pointwise $L^2$-limit of such discrete operators built from an i.i.d. random sample on a smooth compact manifold. Simulation results complementing the limiting distribution results are also presented.

Soil and groundwater contamination is a pervasive problem at thousands of locations across the world. Contaminated sites often require decades to remediate or to monitor natural attenuation. Climate change exacerbates the long-term site management problem because extreme precipitation and/or shifts in precipitation/evapotranspiration regimes could re-mobilize contaminants and proliferate affected groundwater. To quickly assess the spatiotemporal variations of groundwater contamination under uncertain climate disturbances, we developed a physics-informed machine learning surrogate model using U-Net enhanced Fourier Neural Operator (U-FNO) to solve Partial Differential Equations (PDEs) of groundwater flow and transport simulations at the site scale.We develop a combined loss function that includes both data-driven factors and physical boundary constraints at multiple spatiotemporal scales. Our U-FNOs can reliably predict the spatiotemporal variations of groundwater flow and contaminant transport properties from 1954 to 2100 with realistic climate projections. In parallel, we develop a convolutional autoencoder combined with online clustering to reduce the dimensionality of the vast historical and projected climate data by quantifying climatic region similarities across the United States. The ML-based unique climate clusters provide climate projections for the surrogate modeling and help return reliable future recharge rate projections immediately without querying large climate datasets. In all, this Multi-scale Digital Twin work can advance the field of environmental remediation under climate change.

Power transformers are an important component of a nuclear power plant (NPP). Currently, the NPP operates a lot of power transformers with extended service life, which exceeds the designated 25 years. Due to the extension of the service life, the task of monitoring the technical condition of power transformers becomes urgent. An important method for monitoring power transformers is Chromatographic Analysis of Dissolved Gas. It is based on the principle of controlling the concentration of gases dissolved in transformer oil. The appearance of almost any type of defect in equipment is accompanied by the formation of gases that dissolve in oil, and specific types of defects generate their gases in different quantities. At present, at NPPs, the monitoring systems for transformer equipment use predefined control limits for the concentration of dissolved gases in the oil. This study describes the stages of developing an algorithm to detect defects and faults in transformers automatically using machine learning and data analysis methods. Among machine learning models, we trained Logistic Regression, Decision Trees, Random Forest, Gradient Boosting, Neural Networks. The best of them were then combined into an ensemble (StackingClassifier) showing F1-score of 0.974 on a test sample. To develop mathematical models, we used data on the state of transformers, containing time series with values of gas concentrations (H2, CO, C2H4, C2H2). The datasets were labeled and contained four operating modes: normal mode, partial discharge, low energy discharge, low-temperature overheating.

This paper proposes a novel energy storage price arbitrage algorithm combining supervised learning with dynamic programming. The proposed approach uses a neural network to directly predicts the opportunity cost at different energy storage state-of-charge levels, and then input the predicted opportunity cost into a model-based arbitrage control algorithm for optimal decisions. We generate the historical optimal opportunity value function using price data and a dynamic programming algorithm, then use it as the ground truth and historical price as predictors to train the opportunity value function prediction model. Our method achieves 65% to 90% profit compared to perfect foresight in case studies using different energy storage models and price data from New York State, which significantly outperforms existing model-based and learning-based methods. While guaranteeing high profitability, the algorithm is also light-weighted and can be trained and implemented with minimal computational cost. Our results also show that the learned prediction model has excellent transferability. The prediction model trained using price data from one region also provides good arbitrage results when tested over other regions.

Lawrence Livermore National Laboratory has long been one of the world's largest consumers of supercomputing capacity. With computing power of more than 200 petaflops, or 200 billion floating-point operations per second, the U.S. Department of Energy-operated institution runs supercomputers from every major U.S. manufacturer. For the past two years, that lineup has included two newcomers: Cerebras Systems Inc. and SambaNova Systems Inc. The two startups, which have collectively raised more than $1.8 billion in funding, are attempting to upend a market that has been dominated so far by off-the-shelf x86 central processing units and graphics processing units with hardware that's purpose-built for use in artificial intelligence model development and inference processing to run those models. Cerebras says its WSE-2 chip, built on a wafer-scale architecture, can bring 2.6 trillion transistors and 850,000 CPU cores to bear on the task of training neural networks. That's about 500 times as many transistors and 100 times as many cores as are found on a high-end GPU.

Waymo is one step closer to charging passengers for fully driverless rides in San Francisco. The California Public Utilities Commission (CPUC) has granted the company a Driverless Pilot permit, which allows it to pick up passengers in a test vehicle without a driver behind the wheel. By securing the permit, Waymo now has the authority to offer driverless rides throughout San Francisco, portions of Daly City, as well as in portions of Los Altos, Los Altos Hills, Mountain View, Palo Alto and Sunnyvale. Its vehicles are allowed to go as fast as 65 miles per hour and can operate 24/7, but the company can't charge for the rides just yet. Waymo told Engadget that it will begin offering free rides without a driver to select members of the public in the coming weeks.

Data creates an opportunity to refine the conventional methodologies in optimizing the decision-making and evaluating every aspect of operations. The scope of opportunity is usually proportional to the quantity of data available for processing; thus, an efficient computing system plays a significant role in implementing structured architectures for AI-related mechanisms. Despite the breakthroughs and optimizations in cloud computing, the current amount of data is too huge to compute with utmost efficiency. Furthermore, parameters like latency and security become important factors when it comes to the transmission of this huge amount of data. As they say, "when the problem becomes too complicated, the answer lies in the roots."

A new study suggests tactics for machine learning engineers to cut their carbon emissions. Led by David Patterson, researchers at Google and UC Berkeley found that AI developers can shrink a model's carbon footprint a thousand-fold by streamlining architecture, upgrading hardware, and using efficient data centers. The authors examined the total energy used and carbon emitted by five NLP models: GPT-3, GShard, Meena, Switch Transformer, and T5. They reported separate figures for training and inference. The authors joined the Allen Institute and others in calling for greener AI.

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. The proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code \textsc{Gene} show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to about four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.