Dynamic modelling of flexible dispatch in a novel nuclear-solar integrated energy system with thermal energy storage
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Nuclear Science & Technology↗
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Results for “Dynamical systems”
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.
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Optimization of an aerostructural machining process using physics-guided Bayesian stability modelling
Existing algorithms for predicting milling chatter have not been widely adopted in industry since they require specialized instruments to measure the stability inputs. This study describes how the machining process for a meter-scale aluminum aerostructure was optimized using a physics-guided Bayesian stability model. The study was performed in collaboration with an industrial partner on production machines to evaluate the practicality of the proposed method under real-world conditions. For each cutting tool, the Bayesian approach automatically selected a small number of cutting tests, which were monitored using a microphone to observe the chatter frequency. The algorithm learned the system dynamics, cutting forces, and stability map from these test results. A novel algorithm for predicting tool bending stress was incorporated into the test selection algorithm to avoid tool breakage. On average, each set of optimized cutting parameters required less than six tests to identify and were 97% more productive than baseline parameters from the cutting tool manufacturer. The machining program was then further optimized using commercial feedrate scheduling software to remove cutting force spikes and reduce air cutting time. Five components were machined using the optimized process. These results demonstrate the potential for physics-guided Bayesian models to improve productivity in industrial settings.
Cornelius, Aaron [UT Knoxville]↗
Learning turbulent flows with generative models for super resolution and sparse flow reconstruction
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.
Fluid dynamics↗
Trusted Simulation: Considering Model Quality in the Context of User Trust
A high‐quality simulation model should help its users to easily and appropriately calibrate their trust in the model. Traditional evaluation metrics such as validation and robustness are necessary but insufficient for this task. Trust calibration depends on factors like the model's transparency, applicability to intended use, usability, reputation, and consideration of potential bias. This article proposes a framework for designing and evaluating system dynamics models by considering factors that contribute to the proper calibration of user trust. This framework takes inspiration from trusted artificial intelligence, broadening our traditional concept of model quality and explicitly focusing on what users need to consider a model trustworthy and to understand the model's relevance to its intended purpose. The trusted simulation framework can improve our integration of model quality activities throughout the modeling process, leading to more impactful and better‐targeted model design, development, and evaluation.
Naugle, Asmeret Bier [Sandia National Laboratories↗
Quantum computation of SU(2) lattice gauge theory with continuous variables
We present a quantum computational framework for pure SU(2) lattice gauge theory, using continuous variables instead of discrete qubits to represent the infinite-dimensional Hilbert space of the gauge fields. We consider a ladder as well as a two-dimensional grid of plaquettes, detailing the use of gauge fixing to reduce the degrees of freedom and simplify the Hamiltonian. We demonstrate how system dynamics, ground states, and energy gaps can be computed using the continuous-variable approach to quantum computing. Our results indicate that it is feasible to study non-Abelian gauge theories with continuous variables, providing new avenues for understanding the real-time dynamics of quantum field theories.
Gauge Symmetry↗
Characterizing Turbulence at a Forest Edge: Comparing Sub-Filter Scale Turbulence Models in Simulations of Flow over a Canopy
In wildfires, atmospheric turbulence plays a major role in the transfer of turbulent kinetic energy. Understanding how turbulence feeds back into a dynamical system is important, down to the varying small scales of fuel structures (i.e. pine needles, grass). Large eddy simulations (LES) are a common way of numerically representing turbulence. The Smagorinsky model (1963) serves as one of the most studied sub-grid scale representations in LES. In this investigation, the Smagorinsky model was implemented in HIGRAD/FIRETEC, LANL’s coupled fire-atmosphere model. This study was motivated by the need to quantitatively investigate the vorticity budget equation in HIGRAD/FIRETEC. The Smagorinsky turbulent kinetic energy (TKE) was compared to FIRETEC’s 1.5-order TKE eddy-viscosity subgrid-scale model, known as the Linn turbulence model. This was done in simulations of flow over flat terrain with a homogeneous, cuboidal canopy in the center of the domain. Examinations of the modeled vertical TKE profile and turbulent statistics at the leading edge, and throughout the canopy, show that the Smagorinsky model provides comparable results to that of the original closure model posed in FIRETEC.
58 GEOSCIENCES↗
A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs
In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.
creep-fatigue↗
From PINNs to PIKANs: recent advances in physics-informed machine learning
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.
Kolmogorov-Arnold networks↗
D2NO: Efficient handling of heterogeneous input function spaces with distributed deep neural operators
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. We propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. Here, we demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present three numerical examples to validate its performance.
97 MATHEMATICS AND COMPUTING↗
Transient anisotropic kernel for probabilistic learning on manifolds
PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.
Diffusion maps↗
A neural-network-enhanced parameter-varying framework for multi-objective model predictive control applied to buildings
Management of the electrical grid is becoming more complex due to the increased penetration of alternative energy generation technologies and a broadening diversity of electric loads. This complexity creates challenges in balancing demand and generation that can increase the potential for grid instabilities. One effective way to address this issue is to leverage previously unexploited demand flexibility through advanced control strategies. In this work, we propose an advanced control method, called adaptive neural parameter-varying model predictive control (ANPV-MPC), to control the temperature and energy consumption of a building via its Heating, Ventilation, and Air Conditioning system. ANPV-MPC combines key ideas in parameter-varying control, adaptive control, and online learning strategies to bridge the gap between computationally efficient linear model predictive control and more accurate nonlinear model predictive control. The novelty in ANPV-MPC is the use of a physics-inspired Bayesian neural network to estimate the coefficients of the parameter-varying linear control model. The Bayesian neural network additionally provides uncertainty estimates, triggering online training to capture evolving building system conditions. We show that ANPV-MPC can approximate the building system dynamics with a 28.39% higher accuracy than traditional linear model predictive control, resulting in 36.23% better control performance without increasing complexity of the optimal control problem. ANPV-MPC also adapts in real time to previously unseen conditions using online learning, further improving its performance.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Experimental test of model predictive control in a variable air volume system
Model predictive control (MPC) has been widely studied as a promising approach for improving energy efficiency and operational flexibility in buildings, yet its real-world performance for commercial variable air volume (VAV) systems remains insufficiently characterized. In particular, the impacts of model mismatch on control robustness, real-time computational burden, and device-level operation are rarely evaluated using long-term field data. Here, this study presents a comprehensive experimental evaluation of MPC applied to a full-scale VAV system in Oak Ridge National Laboratory’s Flexible Research Platform-2 building with constant cooling/heating temperature setpoints and no occupancy. The study offers three key advantages over existing work: (1) it uses a representative building in a full-scale experimental test, capturing realistic system dynamics and complexity; (2) it evaluates a relatively sophisticated MPC formulation using two different optimization solvers (Gurobi and PSO), fully accounting for computational complexity and methodological diversity; and (3) it systematically assesses potential negative impacts on various building devices, benchmark against a well-established baseline, ASHRAE Guideline 36 (G36). To isolate zone- and air-handling-unit–level supervisory control effects, the supply fan was operated with a fixed static pressure setpoint under all strategies, and the trim-and-response static pressure reset in G36 was not enabled. Results show that MPC maintained thermal comfort while improving energy efficiency. Abrupt solar radiation variations degraded performance. Computation times ranged from ∼1 s (Gurobi) to ∼ 70 s (PSO). Compared with G36, MPC achieves 33% energy savings and reduces median reheat coil output by approximately a factor of 5–10 for a representative cooling day under matched weather conditions. However, it increases the maximum discomfort deviation from 0.5 to 1°C and results in a 32% increase in staging frequency. In addition, PSO-based MPC introduced damper oscillations, also affecting actuator longevity.
ASHRAE guideline 36↗
Estimated attribution of the RFS program on soybean biodiesel in the U.S. using the bioenergy scenario model
Biofuels are supported by various governmental policies in the U.S. and globally as an alternative transportation fuel for environmental, geopolitical, and economic reasons. Much debate surrounds the effectiveness of these policies as well as the overall net environmental effect of increased biofuels use. In the U.S., recent studies have shown that the Renewable Fuels Standard (RFS) Program, overall, may not have been the leading driver of the ethanol industry from 2005 to 2020, contrary to common perception. Similar scrutiny has not been applied to biodiesel. Here, this study uses the Bioenergy Scenario Model, a well-vetted system dynamics model, to retrospectively apportion historical biodiesel production between the RFS Program and other potentially influential drivers, such as the economics of biodiesel vs. diesel, the Biodiesel Tax Credit (BTC), California's Low Carbon Fuel Standard, and other factors. From 2002 to 2020 about 36% of biodiesel production can be attributed to the RFS Program, 35% to the BTC, and the rest to other factors. Thus, the overall effect of the RFS Program appears much larger on biodiesel than on corn ethanol. The finding that the same policy may have very disparate effects on different biofuels helps inform the design of future policies on biofuels.
09 BIOMASS FUELS↗
RandONets: Shallow networks with random projections for learning linear and nonlinear operators
Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.
Interpretable machine learning↗
A safe reinforcement learning algorithm for supervisory control of power plants
Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.
constrained optimization↗
On the effectiveness of neural operators at zero-shot weather downscaling
Machine-learning (ML) methods have shown great potential for weather downscaling. These data-driven approaches provide a more efficient alternative for producing high-resolution weather datasets and forecasts compared to physics-based numerical simulations. Neural operators, which learn solution operators for a family of partial differential equations, have shown great success in scientific ML applications involving physics-driven datasets. Neural operators are grid-resolution-invariant and are often evaluated on higher grid resolutions than they are trained on, i.e., zero-shot super-resolution. Given their promising zero-shot super-resolution performance on dynamical systems emulation, we present a critical investigation of their zero-shot weather downscaling capabilities, which is when models are tasked with producing high-resolution outputs using higher upsampling factors than are seen during training. To this end, we create two realistic downscaling experiments with challenging upsampling factors (e.g., 8x and 15x) across data from different simulations: the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5) and the Wind Integration National Dataset Toolkit. While neural operator-based downscaling models perform better than interpolation and a simple convolutional baseline, we show the surprising performance of an approach that combines a powerful transformer-based model with parameter-free interpolation at zero-shot weather downscaling. We find that this Swin-Transformer-based approach mostly outperforms models with neural operator layers in terms of average error metrics, whereas an Enhanced Super-Resolution Generative Adversarial Network-based approach is better than most models in terms of capturing the physics of the ground truth data. We suggest their use in future work as strong baselines.
17 WIND ENERGY↗
From Latent Dynamics to Meaningful Representations
While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density — a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. Here, we show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A Non‐Intrusive Machine Learning Framework for Debiasing Long‐Time Coarse Resolution Climate Simulations and Quantifying Rare Events Statistics
Abstract Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully‐resolved climate simulations remain computationally intractable, policy makers must rely on coarse‐models to quantify risk for extremes. However, coarse models suffer from inherent bias due to the ignored “sub‐grid” scales. We propose a framework to non‐intrusively debias coarse‐resolution climate predictions using neural‐network (NN) correction operators. Previous efforts have attempted to train such operators using loss functions that match statistics. However, this approach falls short with events that have longer return period than that of the training data, since the reference statistics have not converged. Here, the scope is to formulate a learning method that allows for correction of dynamics and quantification of extreme events with longer return period than the training data. The key obstacle is the chaotic nature of the underlying dynamics. To overcome this challenge, we introduce a dynamical systems approach where the correction operator is trained using reference data and a coarse model simulation nudged toward that reference. The method is demonstrated on debiasing an under‐resolved quasi‐geostrophic model and the Energy Exascale Earth System Model (E3SM). For the former, our method enables the quantification of events that have return period two orders longer than the training data. For the latter, when trained on 8 years of ERA5 data, our approach is able to correct the coarse E3SM output to closely reflect the 36‐year ERA5 statistics for all prognostic variables and significantly reduce their spatial biases.
Barthel Sorensen, B.↗