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Hierarchical Testing of a Hybrid Machine Learning‐Physics Global Atmosphere Model

Machine learning (ML)-based models have demonstrated high skill and computational efficiency, often outperforming conventional physics-based models in weather and subseasonal predictions. While prior studies have assessed their fidelity in capturing synoptic-scale atmospheric dynamics, their performance across timescales and under out-of-distribution forcing, such as +3K or +4K uniform-warming forcings, and the sources of biases remain elusive, to establish the model's reliability for Earth science. Here, we design three sets of experiments targeting synoptic-scale phenomena, interannual variability, and out-of-distribution uniform-warming forcings. We evaluate the Neural General Circulation Model (NeuralGCM), a hybrid model integrating a dynamical core with ML-based component, against observations and physics-based Earth system models (ESMs). At the synoptic scale, NeuralGCM captures the evolution and propagation of extratropical cyclones with performance comparable to ESMs. At the interannual scale, when forced by El Niño-Southern Oscillation sea surface temperature (SST) anomalies, NeuralGCM successfully reproduces associated teleconnection patterns but exhibits deficiencies in capturing nonlinear response. Under out-of-distribution uniform-warming forcings, NeuralGCM simulates similar responses in global-average temperature and precipitation and reproduces large-scale tropospheric circulation features similar to those in ESMs. Notable weaknesses include overestimating the tracks and spatial extent of extratropical cyclones, biases in the teleconnected wave train triggered by tropical SST anomalies, and differences in upper-level warming and stratospheric circulation responses to SST warming compared to physics-based ESMs. The causes of these weaknesses were explored. Despite the noted weaknesses, NeuralGCM reproduces responses across experiments reasonably and performs comparably to ESMs. By integrating a dynamical core with ML, NeuralGCM shows potential for developing ML-based ESMs.

global warming↗

Towards intelligent emergency control for large-scale power systems: Convergence of learning, physics, computing and control

Here, this paper has delved into the pressing need for intelligent emergency control in large-scale power systems, which are experiencing significant transformations and are operating closer to their limits with more uncertainties. Learning-based control methods are promising and have shown effectiveness for intelligent power system control. However, when they are applied to large-scale power systems, there are multifaceted challenges such as scalability, adaptiveness, and security posed by the complex power system landscape, which demand comprehensive solutions. The paper first proposes and instantiates a convergence framework for integrating power systems physics, machine learning, advanced computing, and grid control to realize intelligent grid control at a large scale. Our developed methods and platform based on the convergence framework have been applied to a large (more than 3000 buses) Texas power system, and tested with 56 000 scenarios. Our work achieved a 26% reduction in load shedding on average and outperformed existing rule-based control in 99.7% of the test scenarios. The results demonstrated the potential of the proposed convergence framework and DRL-based intelligent control for the future grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Stable Simulation of the Community Atmosphere Model Using Machine‐Learning Physical Parameterization Trained With Experience Replay

In recent years, machine learning (ML) models have been used to improve physical parameterizations of general circulation models (GCMs). A significant challenge of integrating ML models into GCMs is the online instability when they are coupled for long‐term simulation. We present a new strategy that demonstrates robust online stability when the physical parameterization package of an atmospheric GCM is replaced by a deep ML model. The method uses experience replay with a multistep training scheme of the ML model in which the model's own output at the previous time step is used in the training. Predicted physics tendencies in the replay buffer with the most recent errors in the training iterations are reused, making the ML model learn from its own errors. The training method reduces the gap between the offline and online environments of the ML model. The method is used to train the ML model as the physical parameterization of the Community Atmosphere Model (CAM5) with training data from the Multi‐scale Modeling Framework high resolution simulations. Three 6‐year online simulations of the CAM5 are carried out by using the ML physics package. The simulated spatial distributions of precipitation, surface temperature and zonally averaged atmospheric fields demonstrate overall better accuracy than that of the standard CAM5 and benchmark model even without the use of additional physical constraints or tuning. This work is the first to demonstrate a solution to address the online instability problem in climate modeling with ML physics by using experience replay.

54 ENVIRONMENTAL SCIENCES↗

Learning Physically Interpretable Atmospheric Models From Data With WSINDy

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the weak-form sparse identification of nonlinear dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension.

58 GEOSCIENCES↗

Role of physics in physics-informed machine learning

Physical systems are characterized by inherent symmetries, one of which is encapsulated in the units of their parameters and system states. These symmetries enable a lossless order-reduction, e.g., via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machine learning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/or numerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantly enhance the interpretability and generalizability of ML-discovered secondary laws. Our numerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysis enable both deep neural networks and sparse regression reproduce old results, e.g., Stokes law for a sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction. Furthermore, our results suggest the need to incorporate other physics-based symmetries and invariances into ML-based techniques for equation discovery.

97 MATHEMATICS AND COMPUTING↗

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗

Physics-tailored machine learning reveals unexpected physics in dusty plasmas

Dusty plasma is a mixture of ions, electrons, and macroscopic charged particles that is commonly found in space and planetary environments. The particles interact through Coulomb forces mediated by the surrounding plasma, and as a result, the effective forces between particles can be nonconservative and nonreciprocal. Machine learning (ML) models are a promising route to learn these complex forces, yet their structure should match the underlying physical constraints to provide useful insight. Here, we demonstrate and experimentally validate an ML approach that incorporates physical intuition to infer force laws in a laboratory dusty plasma. Trained on 3D particle trajectories, the model accounts for inherent symmetries, nonidentical particles, and learns the effective nonreciprocal forces between particles with exquisite accuracy (R 2 > 0.99). We validate the model by inferring particle masses in two independent yet consistent ways. The model’s accuracy enables precise measurements of particle charge and screening length, identifying large deviations from common theoretical assumptions. Our ability to identify unknown physics from experimental data demonstrates how ML-powered approaches can guide new routes of scientific discovery in many-body systems. Furthermore, we anticipate our ML approach to be a starting point for inferring laws from dynamics in a wide range of many-body systems, from colloids to living organisms.

Science & Technology - Other Topics↗

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↗

Integrating Learning and Physics based Computation for Fast Online Transient Analysis

In this work, a novel method that integrates learning and physics based computation is developed for greatly accelerating the simulation of full power system transient trajectories. To solve the dynamic algebraic equations, the method replaces the time-consuming dynamic computation for generator dynamics with trained predictors, while retaining the time-efficient algebraic computation of solving AC-power flow (PF) for power systems. In particular, a predictor is trained for each generator, and the system trajectories are computed by alternating steps of calling the predictors and solving AC-PF. The proposed method also allows fully parallelizable training strategies and a flexible trade-off between training time and testing accuracy. Comprehensive evaluations of the proposed method for transient/dynamic contingency analysis of the New York/New England 16-machine 68-bus power systems demonstrate excellent performance and significant acceleration of computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Demonstration of Decentralized Physics-Driven Learning

In typical artificial neural networks, neurons adjust according to global calculations of a central processor, but in the brain, neurons and synapses self-adjust based on local information. Contrastive learning algorithms have recently been proposed to train physical systems, such as fluidic, mechanical, or electrical networks, to perform machine-learning tasks from local evolution rules. However, to date, such systems have only been implemented in silico due to the engineering challenge of creating elements that autonomously evolve based on their own response to two sets of global boundary conditions. Here, we introduce and implement a physics-driven contrastive learning scheme for a network of variable resistors, using circuitry to locally compare the response of two identical networks subjected to the two different sets of boundary conditions. Using this method, our system effectively trains itself, optimizing its resistance values without the use of a central processor or external information storage. Once the system is trained for a specified allostery, regression, or classification task, the task is subsequently performed rapidly and automatically by the physical imperative to minimize power dissipation in response to the given voltage inputs. Here, we demonstrate that, unlike typical computers, such learning systems are robust to extreme damage (and thus manufacturing defects) due to their decentralized learning. Our twin-network approach is therefore readily scalable to extremely large or nonlinear networks, where its distributed nature will be an enormous advantage; a laboratory network of only 500 edges will already outpace its in silico counterpart.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging: Theory, algorithms, and applications

Plug-and-play (PnP) priors constitute one of the most widely used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly successful applications of PnP algorithms include biomicroscopy, computerized tomography (CT), magnetic resonance imaging (MRI), and joint ptychotomography. This article presents a unified and principled review of PnP by tracing its roots, describing its major variations, summarizing main results, and discussing applications in computational imaging. Additionally, we also point the way toward further developments by discussing recent results on equilibrium equations that formulate the problem associated with PnP algorithms.

97 MATHEMATICS AND COMPUTING↗

Differentiable modelling to unify machine learning and physical models for geosciences

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. Here, in this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs.

58 GEOSCIENCES↗

Combining Deep Learning With Physics Based Features in Explosion-Earthquake Discrimination

This paper combines the power of deep-learning with the generalizability of physics-based features, to present an advanced method for seismic discrimination between earthquakes and explosions. The proposed method contains two branches: a deep learning branch operating directly on seismic waveforms or spectrograms, and a second branch operating on physics-based parametric features. These features are high-frequency P/S amplitude ratios and the difference between local magnitude (ML) and coda duration magnitude (MC). The combination achieves better generalization performance when applied to new regions than models that are developed solely with deep learning. Further, we also examined which parts of the waveform data dominate deep learning decisions (i.e., via Grad-CAM). Such visualization provides a window into the black-box nature of the machine-learning models and offers new insight into how the deep learning derived models use data to make decisions.

58 GEOSCIENCES↗

Efficient simulation of optical spectra via machine learning and physical decomposition of environmental effects

Simulations of optical spectra can provide key insights to aid experimental interpretation of electronic excitation phenomena. For chromophores in the condensed phase, these spectra, which incorporate the coupling between electronic excitation and molecular and solvent nuclear motions, can be simulated using excitation energies obtained from molecular dynamics simulations of the chromophore and solvent. Here, we present a hybrid scheme that exploits machine learning and physically informed spectral densities to show that as few as 25 ground and excited state energetic gradient calculations can be used to construct models that accurately predict environment-influenced vibronic coupling in optical spectra. We demonstrate our approach for the green fluorescent protein chromophore in water and the cresyl violet chromophore in methanol. We show that our hybrid approach, employing a machine learning model for the high-frequency spectral density and an ab initio parameterized Debye spectral density for the low-frequency, results in a systematic improvement of the optical absorption lineshape, leading to a simple machine learning scheme that can be used for the simulation of spectral densities and optical spectra.

Snider, Andrew [Univ. of California, Merced, CA (U↗