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At least 91 records · Page 5

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗

Operator learning for energy-efficient building ventilation control with computational fluid dynamics simulation of a real-world classroom

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.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗

Hyperplane decision trees as piecewise linear surrogate models for chemical process design

Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.

Decision trees↗

Hydropower potential derived from streamflow extremes for Alaska, USA

Alaska is an expansive region known for its abundant natural resources, including thousands of miles of streams and rivers. These rivers represent potential opportunities for future hydropower development that could provide reliable energy supply for local communities. There is limited long-term high temporal resolution streamflow data available for the region, making data-driven estimates of potential hydropower and its variability across the state challenging. This study provides a novel data-driven approach for hydropower capacity estimation across Alaska. We use supervised machine learning to develop a relationship between the daily and peak flow duration curves in order to augment the size of our dataset from 44 sites to 67 sites. We perform a stochastic hydropower estimation across the 67 sites and identify approximately 1000 MW of total potential hydropower capacity distributed across these sites. Our study provides the first step towards more comprehensive hydropower estimation for this critical region, highlighting the need for future work integrating high-resolution spatial data, community needs, and economic constraints in estimates of potential hydropower development in Alaska.

Hydropower↗

A portable application framework for energy management and information systems (EMIS) solutions using Brick semantic schema

This paper introduces a portable framework for developing, scaling and maintaining energy management and information systems (EMIS) applications using an ontology-based approach. Key contributions include an interoperable layer based on Brick schema, the formalization of application constraints pertaining metadata and data requirements, and a field demonstration. The framework allows for querying metadata models, fetching data, preprocessing, and analyzing data, thereby offering a modular and flexible workflow for application development. Its effectiveness is demonstrated through a case study involving the development and implementation of a data-driven anomaly detection tool for the photovoltaic systems installed at the Politecnico di Torino, Italy. During eight months of testing, the framework was used to tackle practical challenges including: (i) developing a machine learning-based anomaly detection pipeline, (ii) replacing data-driven models during operation, (iii) optimizing model deployment and retraining, (iv) handling critical changes in variable naming conventions and sensor availability (v) extending the pipeline from one system to additional ones.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Power generation forecasting for solar plants based on Dynamic Bayesian networks by fusing multi-source information

A Dynamic Bayesian network (DBN) model for solar power generation forecasting in solar plants is proposed in this paper. The key idea is to fuse sensor data, operational indicators, meteorological data, lagged output power information, and model errors for more accurate short-term (e.g., hours) and mid-term (e.g., days to weeks) power generation forecasting. The proposed DBN augments automated data-driven structure learning with expert knowledge encoding using continuous and categorical data given constraints to represent causal relationships within a solar inverter system. Additionally, an error compensation mechanism is proposed to capture temporal fluctuation. The effectiveness of the DBN on solar power generation forecasting was evaluated by rolling window analysis with one-year testing data collected from a local solar plant. The proposed DBN is compared with four state-of-art methods including support-vector regression (SVR), k-nearest neighbors (kNN), artificial neural network (ANN), and long short-term memory (LSTM) models. The result show that the proposed DBN achieves better accuracy in general, and it is not as data-hungry as some neural network-based models. The proposed DBN is also shown to have robust and consistent forecasting power with different forecasting horizons. The accuracy is 92% - 95% from one hour to one week ahead forecasting.

14 SOLAR ENERGY↗

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↗

Clustering of red sequence galaxies in the fourth data release of the Kilo-Degree Survey

We present a sample of luminous red sequence galaxies as the basis for a study of the large-scale structure in the fourth data release of the Kilo-Degree Survey. The selected galaxies are defined by a red sequence template, in the form of a data-driven model of the colour-magnitude relation conditioned on redshift. In this work, the red sequence template was built using the broad-band optical+near infrared photometry of KiDS-VIKING and the overlapping spectroscopic data sets. The selection process involved estimating the red sequence redshifts, assessing the purity of the sample and estimating the underlying redshift distributions of redshift bins. After performing the selection, we mitigated the impact of survey properties on the observed number density of galaxies by assigning photometric weights to the galaxies. We measured the angular two-point correlation function of the red galaxies in four redshift bins and constrain the large-scale bias of our red sequence sample assuming a fixed ΛCDM cosmology. We find consistent linear biases for two luminosity-threshold samples (‘dense’ and ‘luminous’). We find that our constraints are well characterised by the passive evolution model.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards a self-driving trigger at the LHC: adaptive response in real time

Real-time data filtering and selection—or trigger—systems at high-throughput scientific facilities such as the experiments at the Large Hadron Collider must process extremely high-rate data streams under stringent bandwidth, latency, and storage constraints. Yet these systems are typically designed as static, hand-tuned menus of selection criteria grounded in prior knowledge and simulation. In this work, we further explore the concept of a self-driving trigger, an autonomous data-filtering framework that reallocates resources and adjusts thresholds dynamically in real-time to optimize signal efficiency, rate stability, and computational cost as instrumentation and environmental conditions evolve. We introduce a benchmark ecosystem to emulate realistic collider scenarios and demonstrate real-time optimization of a menu including canonical energy sum triggers as well as modern anomaly-detection algorithms that target non-standard event topologies using machine learning. Using simulated data streams and publicly available collision data from the Compact Muon Solenoid experiment, we demonstrate the capability to dynamically and automatically optimize trigger performance under specific cost objectives without manual retuning. Our adaptive strategy shifts trigger design from static menus with heuristic tuning to intelligent, automated, data-driven control, unlocking greater flexibility and discovery potential in future high-energy physics analyses.

Emami, Shaghayegh [Michigan U.] (ORCID:00090007589↗

A variational encoder–decoder approach to precise spectroscopic age estimation for large Galactic surveys

Constraints on the formation and evolution of the Milky Way Galaxy require multidimensional measurements of kinematics, abundances, and ages for a large population of stars. Ages for luminous giants, which can be seen to large distances, are an essential component of studies of the Milky Way, but they are traditionally very difficult to estimate precisely for a large data set and often require careful analysis on a star-by-star basis in asteroseismology. Because spectra are easier to obtain for large samples, being able to determine precise ages from spectra allows for large age samples to be constructed, but spectroscopic ages are often imprecise and contaminated by abundance correlations. Here we present an application of a variational encoder–decoder on cross-domain astronomical data to solve these issues. The model is trained on pairs of observations from APOGEE and Kepler of the same star in order to reduce the dimensionality of the APOGEE spectra in a latent space while removing abundance information. The low dimensional latent representation of these spectra can then be trained to predict age with just ∼1000 precise seismic ages. We demonstrate that this model produces more precise spectroscopic ages (∼ 22 per cent overall, ∼ 11 per cent for red-clump stars) than previous data-driven spectroscopic ages while being less contaminated by abundance information (in particular, our ages do not depend on [α/M]). We create a public age catalogue for the APOGEE DR17 data set and use it to map the age distribution and the age-[Fe/H]-[α/M] distribution across the radial range of the Galactic disc.

79 ASTRONOMY AND ASTROPHYSICS↗

EMPDF : inferring the Milky Way mass with data-driven distribution function in phase space

We introduce the emPDF (empirical distribution function), a novel dynamical modelling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state. emPDF determines the best-fitting potential by maximizing the similarity between instantaneous kinematics and the time-averaged phase-space distribution function (DF), which is empirically constructed from observation upon the theoretical foundation of oPDF (Han et al. 2016). This approach eliminates the need for presumed functional forms of DFs or orbit libraries required by conventional DF- or orbit-based methods. emPDF stands out for its flexibility, efficiency, and capability in handling observational effects, making it preferable to the popular Jeans equation or other minimal assumption methods, especially for the Milky Way (MW) outer halo where tracers often have limited sample size and poor data quality. We apply emPDF to infer the MW mass profile using Gaia DR3 data of satellite galaxies and globular clusters, obtaining enclosed masses of M (,r) = 26±8, 46±8, 90±13⁠, and 149±40 x 10 10 M ⊙ at r = 30, 50, 100⁠, and 200 kpc, respectively. These are consistent with the updated constraints from simulation-informed DF fitting (Li et al. 2020). While the simulation-informed DF offers superior precision owing to the additional information extracted from simulations, emPDF is independent of such supplementary knowledge and applicable to general tracer populations. emPDF is currently implemented for tracers with complete 6D kinematics within spherical potentials, but it can potentially be extended to address more general problems.

Astrophysics of Galaxies (astro-ph.GA)↗

Dark Energy Survey Year 3 results: Simulation-based 𝑤CDM inference from weak lensing and galaxy clustering maps with deep learning: Analysis design

Data-driven approaches using deep learning are emerging as powerful techniques to extract non-Gaussian information from cosmological large-scale structure. Here, this work presents the first simulation-based inference (SBI) pipeline that combines weak lensing and galaxy clustering maps in a realistic Dark Energy Survey Year 3 (DES Y3) configuration and serves as preparation for a forthcoming analysis of the survey data. We develop a scalable forward model based on the CosmoGridV1 suite of N-body simulations to generate over one million self-consistent mock realizations of DES Y3 at the map level. Leveraging this large dataset, we train deep graph convolutional neural networks on the full survey footprint in spherical geometry to learn low-dimensional features that approximately maximize mutual information with target parameters. These learned compressions enable neural density estimation of the implicit likelihood via normalizing flows in a ten-dimensional parameter space spanning cosmological 𝑤CDM, intrinsic alignment, and linear galaxy bias parameters, while marginalizing over baryonic, photometric redshift, and shear bias nuisances. To ensure robustness, we extensively validate our inference pipeline using synthetic observations derived from both systematic contaminations in our forward model and independent Buzzard galaxy catalogs. Our forecasts yield significant improvements in cosmological parameter constraints, achieving 2−3× higher figures of merit in the 𝛺 𝑚 − 𝑆 8 plane relative to our implementation of baseline two-point statistics and effectively breaking parameter degeneracies through probe combination. These results demonstrate the potential of SBI analyses powered by deep learning for upcoming Stage-IV wide-field imaging surveys.

Thomsen, A. [Zurich, ETH] (ORCID:0000000203099021)↗

Code for the manuscript "Lagrangian Large Eddy Simulations vis Physics-informed Machine Learning"

We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Tian, Yifeng↗

Joint physics-based and data-driven time-lapse seismic inversion: Mitigating data scarcity

In carbon capture and sequestration (CCS), developing rapid and effective imaging techniques is crucial for real-time monitoring of the spatial and temporal dynamics of CO 2 propagation during/after injection. With continuing improvements in computational power and data storage, data-driven techniques based on machine learning (ML) have been effectively applied to seismic inverse problems. In particular, ML helps alleviate the ill-posedness and high computational cost of full-waveform inversion (FWI). However, such data-driven inversion techniques require massive high-quality training data sets to ensure prediction accuracy, which hinders their application to time-lapse monitoring of CO 2 sequestration. We propose an efficient “hybrid” time-lapse workflow that combines physics-based FWI and data-driven ML inversion. The scarcity of the available training data is addressed by developing a new data-generation technique with physics constraints. The method is vali dated on a synthetic CO 2 -sequestration model based on the Kimberlina storage reservoir in California. The proposed approach is shown to synthesize a large volume of high-quality, physically realistic training data, which is critically important in accurately characterizing the CO 2 movement in the reservoir. In conclusion, the developed hybrid methodology can also simultaneously predict the variations in velocity and saturation and achieve high spatial resolution in the presence of realistic noise in the data.

58 GEOSCIENCES↗

Constructing Data-Driven Predictions at the Far Detector for NOvA's Neutrino Oscillation Analysis.

NOvA, is a two-detector, long-baseline neutrino oscillation experiment located at Fermilab, Batavia, IL, USA. It is designed primarily to constrain neutrino oscillation parameters using $\nu_\mu \ (\bar{\nu}_\mu)$ disappearance and $\nu_e \ (\bar{\nu}_e)$ appearance data. The Neutrinos at Main Injector (NuMI) beamline at Fermilab provides a high purity 900 KW intense beam of neutrinos and anti-neutrinos to NOvA. The NOvA Near Detector, located 100m underground and 1km away from the beam source, observes the un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ and beam $\nu_e \ (\bar{\nu}_e)$ event spectrum. The Far Detector, located in Ash River, MN, USA, is 809 km from the ND and records the oscillated $\nu_e \ (\bar{\nu}_e)$ and the un-oscillated $\nu_\mu \ (\bar{\nu}_\mu)$ event spectrum. NOvA uses a data-driven technique called extrapolation to predict the expected number of $\nu_\mu \ (\bar{\nu}_\mu)$ and $\nu_e \ (\bar{\nu}_e)$ events at the Far Detector using the Near Detector data. The use of data from a functionally equivalent Near Detector provides a powerful constraint on the systematic uncertainties in NOvA neutrino oscillation analyses. As NOvA continues to add data statistics, a robust constraint on systematics becomes more crucial for neutrino oscillation analysis. The details of the NOvA neutrino oscillation analysis framework and how it constrains dominant systematic uncertainties using the Near Detector data will be discussed in this poster.

43 PARTICLE ACCELERATORS↗

Probabilistic Deliverability Assessment of Distributed Energy Resources via Scenario-Based AC Optimal Power Flow

As electric grids decarbonize and distributed energy resources (DERs) become increasingly prevalent, interconnection assessments must evolve to reflect operational variability and control flexibility. This paper highlights key modeling limitations observed in practice and reviews approaches for modeling uncertainty. It then introduces a Probabilistic Deliverability Assessment (PDA) framework designed to complement and extend existing procedures. The framework integrates scenario-based AC optimal power flow (AC OPF), corrective dispatch, and optional multi-temporal constraints. Together, these form a structured methodology for quantifying DER utilization, deliverability, and reliability under uncertainty in load, generation, and topology. Outputs include interpretable metrics with confidence intervals that inform siting decisions and evaluate compliance with reliability thresholds across sampled operating conditions. A case study on Puerto Rico’s publicly available bulk power system model demonstrates the framework’s application using minimal input data, consistent with current interconnection practice. Across staged fossil generation retirements, the PDA identifies high-value DER sites and regions requiring additional reactive power support. Results are presented through mean dispatch signals, reliability metrics, and geospatial visualizations, demonstrating how the framework provides transparent, data-driven siting recommendations. The framework’s modular design supports incremental adoption within existing workflows, encouraging broader use of AC OPF in interconnection and planning contexts.

14 SOLAR ENERGY↗

Efficient Reinforcement Learning for Real-Time Hardware-Based Energy System Experiments: Preprint

In the context of urgent climate challenges and the pressing need for rapid technology development, Reinforcement Learning (RL) stands as a compelling data-driven method for controlling real-world physical systems. However, RL implementation often entails time-consuming and computationally intensive data collection and training processes, rendering them inefficient for real-time applications that lack non-real-time models. To address these limitations, real-time emulation techniques have emerged as valuable tools for the lab-scale rapid prototyping of intricate energy systems. While emulated systems offer a bridge between simulation and reality, they too face constraints, hindering comprehensive characterization, testing, and development. In this research, we construct a surrogate model using limited data from simulated systems, enabling an efficient and effective training process for a Double Deep Q-Network (DDQN) agent for future deployment. Our approach is illustrated through a hydropower application, demonstrating the practical impact of our approach on climate-related technology development.

deep Q-learning↗