Neural operators for accelerated uncertainty quantification in ice-sheet modeling
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Explore the source record for details and available documents.
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Neural net control of operations in a small subsonic/transonic/supersonic wind tunnel at Lewis Research Center is discussed. The tunnel and the layout for neural net control or control by other parallel processing techniques are described. The tunnel is an affordable, multiuser platform for testing instrumentation and components, as well as parallel processing and control strategies. Neural nets have already been tested on archival schlieren and holographic visualizations from this tunnel as well as recent supersonic and transonic shadowgraph. This paper discusses the performance of neural nets for interpreting shadowgraph images in connection with a recent exercise for tuning the tunnel in a subsonic/transonic cascade mode of operation. That mode was operated for performing wake surveys in connection with NASA's Advanced Subsonic Technology (AST) noise reduction program. The shadowgraph was presented to the neural nets as 60 by 60 pixel arrays. The outputs were tunnel parameters such as valve settings or tunnel state identifiers for selected tunnel operating points, conditions, or states. The neural nets were very sensitive, perhaps too sensitive, to shadowgraph pattern detail. However, the nets exhibited good immunity to variations in brightness, to noise, and to changes in contrast. The nets are fast enough so that ten or more can be combined per control operation to interpret flow visualization data, point sensor data, and model calculations. The pattern sensitivity of the nets will be utilized and tested to control wind tunnel operations at Mach 2.0 based on shock wave patterns.
Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.
Neural operators are promising surrogates for dynamical systems but when trained with standard L 2 losses they tend to oversmooth fine-scale turbulent structures. Here, we show that combining operator learning with generative modeling overcomes this limitation. We consider three practical turbulent-flow challenges where conventional neural operators fail: spatio-temporal super-resolution, forecasting, and sparse flow reconstruction. For Schlieren jet super-resolution, an adversarially trained neural operator (adv-NO) reduces the energy-spectrum error by 15 × while preserving sharp gradients at neural operator-like inference cost. For 3D homogeneous isotropic turbulence, adv-NO trained on only 160 timesteps from a single trajectory forecasts accurately for five eddy-turnover times and offers 114 × wall-clock speed-up at inference than the baseline diffusion-based forecasters, enabling near-real-time rollouts. For reconstructing cylinder wake flows from highly sparse Particle Tracking Velocimetry-like inputs, a conditional generative model infers full 3D velocity and pressure fields with correct phase alignment and statistics. These advances enable accurate reconstruction and forecasting at low compute cost, bringing near-real-time analysis and control within reach in experimental and computational fluid mechanics.
Rapid simulation of the spatiotemporal evolution of pressure & saturation for SACROC 1. Neural operator was trained on only 153 simulation runs 2. Trained to account for heterogeneity and variations/uncertainties in engineering, fluids, and geology 3. Pressure forecast has less than 1% error 4. Saturation forecast has less than 2% error 5. Traditional simulator takes 1 hour for a single scenario, while neural operator takes less than 1 minute. Rapid simulation of the spatiotemporal evolution of pressure & saturation for IBDP 1. Transfer Learning was implemented on the SACROC-based Neural Operator that was trained on only 20 simulation runs for IBDP Site 2. SACROC and IBDP Sites have several significant differences in geology and engineering parameters. 3. Pressure forecast has less than 5 psi error 4. Saturation forecast has less than 7% error 5. Traditional simulator takes 1 hour for a single scenario, while neural operator takes less than 1 minute and only 20 simulations for training/validation.
Energy-efficient ventilation control plays an important role in reducing building energy consumption while ensuring occupant health and comfort. While Computational Fluid Dynamics (CFD) simulations provide detailed and physically accurate representations of indoor airflow, their high computational cost limits their use in real-time building control. In this work, we present a neural operator learning framework that combines the physical accuracy of CFD with the computational efficiency of machine learning to enable building ventilation control with the high-fidelity fluid dynamics models. Our method jointly optimizes the airflow supply rates and vent angles to reduce energy use and adhere to air quality constraints. We train an ensemble of neural operator transformer models to learn the mapping from building control actions to airflow fields using high-resolution CFD data. This learned neural operator is then embedded in an optimization-based control framework for building ventilation control. Experimental results show that our approach achieves significant energy savings compared to maximum airflow rate control, rule-based control, as well as data-driven control methods using spatially averaged CO 2 prediction and deep learning–based reduced-order models, while consistently maintaining safe indoor air quality. These results highlight the practicality and scalability of our method in maintaining energy efficiency and indoor air quality in real-world buildings.
Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step sizes during rollout, which limits their ability to adapt to varying temporal complexity and often leads to error accumulation. In this work, we propose the Time-Adaptive Transformer with Neural Taylor Expansion (TANTE), a novel operator-learning framework that produces continuous-time predictions with adaptive step sizes. TANTE predicts future states by performing a Taylor expansion at the current state, where neural networks learn both the higher-order temporal derivatives and the local radius of convergence. This allows the model to dynamically adjust its rollout based on the local behavior of the solution, thereby reducing cumulative error and improving computational efficiency. We demonstrate the effectiveness of TANTE across a wide range of PDE benchmarks, achieving superior accuracy and adaptability compared to fixed-step baselines, delivering accuracy gains of 60-80 % and speed-ups of 30-40 % at inference time.
With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. Here, we propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework’s uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.
A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.
Directional permeability variations, which govern directional fluid flow in porous media with anisotropy, are important to accurately predict flow behavior, reactive transport, and fluid–solid interactions for various processes such as enhanced geothermal systems, energy storage devices, and biological systems. However, the intricate architecture of porous media makes it difficult to predict directional permeabilities. In this work, we present a novel machine learning (ML) framework, AnisONet, built upon an integration of a convolutional neural network, Swin transformer, and the deep operator network architecture, designed to predict anisotropic permeability and upscale predictions to larger spatial domains. First, AnisONet was evaluated with three classes of two-dimensional (2D) porous media, including synthetic circular and elliptical grains and natural sandstone grains from micro-computed tomography images. A lattice Boltzmann model (LBM) was used to calculate directional permeabilities at every 10° angle, producing 19 data points per image of porous media. AnisONet is then trained to predict permeability as a function of rotation angle. AnisONet showed strong predictive capability of directional permeability. Second, we tested our model for five upscaling cases with a large image size in the finite-element method (FEM) for 2D Darcy flow with various permeability tensor construction methods. Overall, upscaled permeability tensors in FEM simulations produce a reasonably good match with LBM results, highlighting the importance of selecting appropriate tensor formation strategies for accurate permeability upscaling. AnisONet, as a directional permeability estimator, could be further developed for more complex geometries, with the potential to develop a foundational ML model for various applications in porous media.
This project helped address the growing need for efficient and scalable models to support geological carbon and energy storage, which are crucial for achieving net-zero emissions. Traditionally accurate high-fidelity numerical models have been used to simulate relevant storage processes under a handful of processes, however such models are computationally demanding, making uncertainty quantification impractical. Consequently, we first developed a machine learning framework, based on Graph Neural Operators (GNOs), to improving the accuracy of model predictions for a fixed computational budget. We then developed an Ensemble of Improved Neural Operators (ENO), which uses bagging and Monte Carlo dropout techniques, to further improve prediction accuracy. Lastly, we developed the way to explain progressive transfer learning methods to reduce the amount of training data and computational cost of training (i.e., reduce trainable parameters) when using our models for multiple storage sites. Our numerical investigation, which used real-world case studies, demonstrated that our framework can significantly improve the safety and efficiency of geological storage operations, with potential applications in other domains such as geothermal reservoirs and climate modeling.
Abstract Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.
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