arXiv subjects

J. Nathan Kutz

Publications and source records attributed to J. Nathan Kutz.

At least 37 records · Page 2Linked to original sources

arXiv2026

The Seismic Wavefield Common Task Framework

Seismology faces fundamental challenges in state forecasting and reconstruction (e.g., earthquake early warning and ground motion prediction) and managing the parametric variability of source locations, mechanisms, and Earth models (e.g., subsurface structure and topography effects). Addressing these with simulations is hindered by their massive scale, both in synthetic data volumes and numerical complexity, while real-data efforts are constrained by models that inadequately reflect the Earth's complexity and by sparse sensor measurements from the field. Recent machine learning (ML) efforts offer promise, but progress is obscured by a lack of proper characterization, fair reporting, and rigorous comparisons. To address this, we introduce a Common Task Framework (CTF) for ML for seismic wavefields, demonstrated here on three distinct wavefield datasets. Our CTF features a curated set of datasets at various scales (global, crustal, and local) and task-specific metrics spanning forecasting, reconstruction, and generalization under realistic constraints such as noise and limited data. Inspired by CTFs in fields like natural language processing, this framework provides a structured and rigorous foundation for head-to-head algorithm evaluation. We evaluate various methods for reconstructing seismic wavefields from sparse sensor measurements, with results illustrating the CTF's utility in revealing strengths, limitations, and suitability for specific problem classes. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigor and reproducibility in scientific ML.

cs.LG↗

arXiv2026

Signature of glassy dynamics in dynamic modes decompositions

Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic relaxation have also been noted, for example, in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study theoretically, but data-driven methods are emerging as a promising alternative that may aid in their analysis. Here, we characterize glassy dynamics using the dynamic mode decomposition, a data-driven spectral computation that approximates the Koopman spectrum. We show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation, and thus, we propose a model-agnostic signature for robustly detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of a one-dimensional ODE and a high-dimensional example of coupled oscillators.

cond-mat.dis-nn↗

arXiv2026

From Models To Experiments: Shallow Recurrent Decoder Networks on the DYNASTY Experimental Facility

The Shallow Recurrent Decoder networks are a novel paradigm recently introduced for state estimation, combining sparse observations with high-dimensional model data. This architecture features important advantages compared to standard data-driven methods including: the ability to use only three sensors (even randomly selected) for reconstructing the entire dynamics of a physical system; the ability to train on compressed data spanned by a reduced basis; the ability to measure a single field variable (easy to measure) and reconstruct coupled spatio-temporal fields that are not observable and minimal hyper-parameter tuning. This approach has been verified on different test cases within different fields including nuclear reactors, even though an application to a real experimental facility, adopting the employment of in-situ observed quantities, is missing. This work aims to fill this gap by applying the Shallow Recurrent Decoder architecture to the DYNASTY facility, built at Politecnico di Milano, which studies the natural circulation established by internally heated fluids for Generation IV applications, especially in the case of Circulating Fuel reactors. The RELAP5 code is used to generate the high-fidelity data, and temperature measurements extracted by the facility are used as input for the state estimation. The results of this work will provide a validation of the Shallow Recurrent Decoder architecture to engineering systems, showing the capabilities of this approach to provide and accurate state estimation.

cs.LG↗

arXiv2026

LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)

Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet approximating the complete spatio-temporal trajectory is essential for mechanistic insight and understanding, model calibration, and operational decision-making. We introduce LAPIS-SHRED (LAtent Phase Inference from Short time sequence using SHallow REcurrent Decoders), a modular architecture that reconstructs and/or forecasts complete spatiotemporal dynamics from sparse sensor observations confined to short temporal windows. LAPIS-SHRED operates through a three-stage pipeline: (i) a SHRED model is pre-trained entirely on simulation data to map sensor time-histories into a structured latent space, (ii) a temporal sequence model, trained on simulation-derived latent trajectories, learns to propagate latent states forward or backward in time to span unobserved temporal regions from short observational time windows, and (iii) at deployment, only a short observation window of hyper-sparse sensor measurements from the true system is provided, from which the frozen SHRED model and the temporal model jointly reconstruct or forecast the complete spatiotemporal trajectory. The framework supports bidirectional inference, inherits data assimilation and multiscale reconstruction capabilities from its modular structure, and accommodates extreme observational constraints including single-frame terminal inputs. We evaluate LAPIS-SHRED on six experiments spanning complex spatio-temporal physics: turbulent flows, multiscale propulsion physics, volatile combustion transients, and satellite-derived environmental fields, highlighting a lightweight, modular architecture suited for operational settings where observation is constrained by physical or logistical limitations.

cs.LG↗

arXiv2026

OpenReservoirComputing: GPU-Accelerated Reservoir Computing in JAX

OpenReservoirComputing (ORC) is a Python library for reservoir computing (RC) written in JAX (Bradbury et al. 2018) and Equinox (Kidger and Garcia 2021). JAX is a Python library for high-performance numerical computing that enables automatic differentiation, just-in-time (JIT) compilation, and GPU/TPU acceleration, while Equinox is a neural network framework for JAX. RC is a form of machine learning that functions by lifting a low-dimensional sequence or signal into a high-dimensional dynamical system and training a simple, linear readout layer from the high-dimensional dynamics back to a lower-dimensional quantity of interest. The most common application of RC is time-series forecasting, where the goal is to predict a signal's future evolution. RC has achieved state-of-the-art performance on this task, particularly when applied to chaotic dynamical systems. In addition, RC approaches can be adapted to perform classification and control tasks. ORC provides both modular components for building custom RC models and built-in models for forecasting, classification, and control. By building on JAX and Equinox, ORC offers GPU acceleration, JIT compilation, and automatic vectorization. These capabilities make prototyping new models faster and enable larger and more powerful reservoir architectures. End-to-end differentiability also enables seamless integration with other deep learning models built with Equinox.

cs.LG↗

arXiv2026

The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)

This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 with the goal of understanding how the MPS domains (Astronomy, Chemistry, Materials Research, Mathematical Sciences, and Physics) can best capitalize on, and contribute to, the future of AI. We present here a summary and snapshot of the MPS community's perspective, as of Spring/Summer 2025, in a rapidly developing field. The link between AI and MPS is becoming increasingly inextricable; now is a crucial moment to strengthen the link between AI and Science by pursuing a strategy that proactively and thoughtfully leverages the potential of AI for scientific discovery and optimizes opportunities to impact the development of AI by applying concepts from fundamental science. To achieve this, we propose activities and strategic priorities that: (1) enable AI+MPS research in both directions; (2) build up an interdisciplinary community of AI+MPS researchers; and (3) foster education and workforce development in AI for MPS researchers and students. We conclude with a summary of suggested priorities for funding agencies, educational institutions, and individual researchers to help position the MPS community to be a leader in, and take full advantage of, the transformative potential of AI+MPS.

cs.AI↗

arXiv2026

Experimental Modal Analysis for engineering structures via time-delay Dynamic Mode Decomposition with Control

Experimental Modal Analysis (EMA) has been widely used to identify structural dynamic properties, including natural frequencies, damping ratios, and mode shapes, for structural integrity assessment. The Poly-reference Least Squares Complex Frequency (pLSCF) method is one of the most widely adopted approaches for EMA because of its strong ability to separate closely spaced modes and its robustness to measurement noise. However, pLSCF-based EMA is generally limited to low-dimensional cases with a small number of measurement points, as its computational cost increases rapidly for high-dimensional or continuous structural measurements, particularly with increasing model order. To overcome this limitation, this paper develops a high-dimensional EMA framework based on Dynamic Mode Decomposition with control (DMDc), a powerful data-driven technique originally developed in fluid dynamics, for modal identification under high-dimensional measurement scenarios. Specifically, the relationship between pLSCF and time-delay DMDc is clarified through the discrete state-space representation of the auto-regressive with exogenous inputs (ARX) model for linear systems. By showing that both methods describe the same physical dynamics of the structure, this study provides a physics-based rationale for applying time-delay DMDc to EMA. The capability and advantages of time-delay DMDc for modal parameter identification in both low- and high-dimensional measurements are validated through numerical simulations of a 6-DOF system and experiments on a cantilever beam using a digital camera. The results demonstrate that time-delay DMDc enables robust and reliable modal parameter identification, effectively addressing high-dimensional EMA problems that are difficult for conventional pLSCF and highlighting its potential for real-world structural dynamics applications.

eess.SY↗

arXiv2026

An Interpretable Data-Driven Model of the Flight Dynamics of Hawks

Despite significant analysis of bird flight, generative physics models for flight dynamics do not currently exist. Yet the underlying mechanisms responsible for various flight manoeuvres are important for understanding how agile flight can be accomplished. Even in a simple flight, multiple objectives are at play, complicating analysis of the overall flight mechanism. Using the data-driven method of dynamic mode decomposition (DMD) on motion capture recordings of hawks, we show that multiple behavioral states such as flapping, turning, landing, and gliding, can be modeled by simple and interpretable modal structures (i.e. the underlying wing-tail shape) which can be linearly combined to reproduce the experimental flight observations. Moreover, the DMD model can be used to extrapolate naturalistic flapping. Flight is highly individual, with differences in style across the hawks, but we find they share a common set of dynamic modes. The DMD model is a direct fit to data, unlike traditional models constructed from physics principles which can rarely be tested on real data and whose assumptions are typically invalid in real flight. The DMD approach gives a highly accurate reconstruction of the flight dynamics with only three parameters needed to characterize flapping, and a fourth to integrate turning manoeuvres. The DMD analysis further shows that the underlying mechanism of flight, much like simplest walking models, displays a parametric coupling between dominant modes suggesting efficiency for locomotion.

q-bio.QM↗

arXiv2026

A joint optimization approach to identifying sparse dynamics using least squares kernel collocation

We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with techniques from reproducing kernel Hilbert space (RKHS) theory for estimating the state and discretizing the ODE. Our numerical experiments reveal that the proposed strategy leads to significant gains in terms of accuracy, sample efficiency, and robustness to noise, both in terms of learning the equation and estimating the unknown states. This work demonstrates capabilities well beyond existing and widely used algorithms while extending the modeling flexibility of other recent developments in equation discovery.

stat.ME↗

arXiv2026

SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework

Bridging the gap between data-rich training regimes and observation-sparse deployment conditions remains a central challenge in spatiotemporal field reconstruction, particularly when target domains exhibit distributional shifts, heterogeneous structure, and multi-scale dynamics absent from available training data. We present SENDAI, a hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework that reconstructs full spatial states from hyper sparse sensor observations by combining simulation-derived priors with learned discrepancy corrections. We demonstrate the performance on satellite remote sensing, reconstructing MODIS (Moderate Resolution Imaging Spectroradiometer) derived vegetation index fields across six globally distributed sites. Using seasonal periods as a proxy for domain shift, the framework consistently outperforms established baselines that require substantially denser observations -- SENDAI achieves a maximum SSIM improvement of 185% over traditional baselines and a 36% improvement over recent high-frequency-based methods. These gains are particularly pronounced for landscapes with sharp boundaries and sub-seasonal dynamics; more importantly, the framework effectively preserves diagnostically relevant structures -- such as field topologies, land cover discontinuities, and spatial gradients. By yielding corrections that are more structurally and spectrally separable, the reconstructed fields are better suited for downstream inference of indirectly observed variables. The results therefore highlight a lightweight and operationally viable framework for sparse-measurement reconstruction that is applicable to physically grounded inference, resource-limited deployment, and real-time monitor and control.

cs.LG↗

arXiv2026

Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Engines

Bridging the sim2real gap between computationally inexpensive models and complex physical systems remains a central challenge in machine learning applications to engineering problems, particularly in multi-scale settings where reduced-order models typically capture only dominant dynamics. In this work, we present Cheap2Rich, a multi-scale data assimilation framework that reconstructs high-fidelity state spaces from sparse sensor histories by combining a fast low-fidelity prior with learned, interpretable discrepancy corrections. We demonstrate the performance on rotating detonation engines (RDEs), a challenging class of systems that couple detonation-front propagation with injector-driven unsteadiness, mixing, and stiff chemistry across disparate scales. Our approach successfully reconstructs high-fidelity RDE states from sparse measurements while isolating physically meaningful discrepancy dynamics associated with injector-driven effects. The results highlight a general multi-fidelity framework for data assimilation and system identification in complex multi-scale systems, enabling rapid design exploration and real-time monitoring and control while providing interpretable discrepancy dynamics. Code for this project is is available at: github.com/kro0l1k/Cheap2Rich.

cs.LG↗

arXiv2026

Terrain-Adaptive Mobile 3D Printing with Hierarchical Control

Mobile 3D printing on unstructured terrain remains challenging due to the conflict between platform mobility and deposition precision. Existing gantry-based systems achieve high accuracy but lack mobility, while mobile platforms struggle to maintain print quality on uneven ground. We present a framework that tightly integrates AI-driven disturbance prediction with multi-modal sensor fusion and hierarchical hardware control, forming a closed-loop perception-learning-actuation system. The AI module learns terrain-to-perturbation mappings from IMU, vision, and depth sensors, enabling proactive compensation rather than reactive correction. This intelligence is embedded into a three-layer control architecture: path planning, predictive chassis-manipulator coordination, and precision hardware execution. Through outdoor experiments on terrain with slopes and surface irregularities, we demonstrate sub-centimeter printing accuracy while maintaining full platform mobility. This AI-hardware integration establishes a practical foundation for autonomous construction in unstructured environments.

cs.RO↗

arXiv2026

Data-driven methods to discover stable linear models of the helicity injectors on HIT-SIU

Accurate and efficient circuit models are necessary to control the power electronic circuits found on plasma physics experiments. Tuning and controlling the behavior of these circuits is inextricably linked to plasma performance. Linear models are greatly preferred for control applications due to their well-established performance guarantees, but they typically fail to capture nonlinear dynamics and changes in experimental parameters. Data-driven system identification can help mitigate these shortcomings by learning interpretable and accurate reduced-order models of a complex system, in this case the injector circuits of the Helicity Injected Torus - Steady Inductive Upgrade (HIT-SIU) experiment. Specifically, the Bagging Optimized Dynamic Mode Decomposition (BOP-DMD), is leveraged to learn stable, reduced order models of the interaction between the spheromak plasma formed in the confinement volume, and the injector circuits of the device. BOP-DMD is trained and evaluated on an analytic model of the vacuum dynamics of the injector circuits of HIT-SIU, as well as an analytic linear reduced-order model for the injector dynamics when a plasma is present. BOP-DMD is then fit on experimental data, both on shots with and without a plasma in the confinement volume. In doing so, we demonstrate the capability of data-driven methods to produce stable, linear models for control and uncertainty quantification in plasma experiments.

physics.plasm-ph↗

arXiv2025

Information theory and discriminative sampling for model discovery

Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables, or measure how different initial trajectories or temporal segments of a trajectory contribute to learning or inferring system dynamics. In this work, we leverage the Fisher Information Matrix (FIM) within the data-driven framework of {\em sparse identification of nonlinear dynamics} (SINDy). We visualize information patterns in chaotic and non-chaotic systems for both single trajectories and multiple initial conditions, demonstrating how information-based analysis can improve sampling efficiency and enhance model performance by prioritizing more informative data. The benefits of statistical bagging are further elucidated through spectral analysis of the FIM. We also illustrate how Fisher information and entropy metrics can promote data efficiency in three scenarios: when only a single trajectory is available, when a tunable control parameter exists, and when multiple trajectories can be freely initialized. As data-driven model discovery continues to gain prominence, principled sampling strategies guided by quantifiable information metrics offer a powerful approach for improving learning efficiency and reducing data requirements.

cs.IT↗

arXiv2025

T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders

SHallow REcurrent Decoders (SHRED) are effective for system identification and forecasting from sparse sensor measurements. Such models are light-weight and computationally efficient, allowing them to be trained on consumer laptops. SHRED-based models rely on Recurrent Neural Networks (RNNs) and a simple Multi-Layer Perceptron (MLP) for the temporal encoding and spatial decoding respectively. Despite the relatively simple structure of SHRED, they are able to predict chaotic dynamical systems on different physical, spatial, and temporal scales directly from a sparse set of sensor measurements. In this work, we modify SHRED by leveraging transformers (T-SHRED) embedded with symbolic regression for the temporal encoding, circumventing auto-regressive long-term forecasting for physical data. This is achieved through a new sparse identification of nonlinear dynamics (SINDy) attention mechanism into T-SHRED to impose sparsity regularization on the latent space, which also allows for immediate symbolic interpretation. Symbolic regression improves model interpretability by learning and regularizing the dynamics of the latent space during training. We analyze the performance of T-SHRED on three different dynamical systems ranging from low-data to high-data regimes.

cs.LG↗

arXiv2025

Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms

Machine learning (ML) is transforming modeling and control in the physical, engineering, and biological sciences. However, rapid development has outpaced the creation of standardized, objective benchmarks - leading to weak baselines, reporting bias, and inconsistent evaluations across methods. This undermines reproducibility, misguides resource allocation, and obscures scientific progress. To address this, we propose a Common Task Framework (CTF) for scientific machine learning. The CTF features a curated set of datasets and task-specific metrics spanning forecasting, state reconstruction, and generalization under realistic constraints, including noise and limited data. Inspired by the success of CTFs in fields like natural language processing and computer vision, our framework provides a structured, rigorous foundation for head-to-head evaluation of diverse algorithms. As a first step, we benchmark methods on two canonical nonlinear systems: Kuramoto-Sivashinsky and Lorenz. These results illustrate the utility of the CTF in revealing method strengths, limitations, and suitability for specific classes of problems and diverse objectives. Next, we are launching a competition around a global real world sea surface temperature dataset with a true holdout dataset to foster community engagement. Our long-term vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets that raise the bar for rigor and reproducibility in scientific ML.

cs.CE↗

arXiv2025

Data assimilation and discrepancy modeling with shallow recurrent decoders

The requirements of modern sensing are rapidly evolving, driven by increasing demands for data efficiency, real-time processing, and deployment under limited sensing coverage. Complex physical systems are often characterized through the integration of a limited number of point sensors in combination with scientific computations which approximate the dominant, full-state dynamics. Simulation models, however, inevitably neglect small-scale or hidden processes, are sensitive to perturbations, or oversimplify parameter correlations, leading to reconstructions that often diverge from the reality measured by sensors. This creates a critical need for data assimilation, the process of integrating observational data with predictive simulation models to produce coherent and accurate estimates of the full state of complex physical systems. We propose a machine learning framework for Data Assimilation with a SHallow REcurrent Decoder (DA-SHRED) which bridges the simulation-to-real (SIM2REAL) gap between computational modeling and experimental sensor data. For real-world physics systems modeling high-dimensional spatiotemporal fields, where the full state cannot be directly observed and must be inferred from sparse sensor measurements, we leverage the latent space learned from a reduced simulation model via SHRED, and update these latent variables using real sensor data to accurately reconstruct the full system state. Furthermore, our algorithm incorporates a sparse identification of nonlinear dynamics based regression model in the latent space to identify functionals corresponding to missing dynamics in the simulation model. We demonstrate that DA-SHRED successfully closes the SIM2REAL gap and additionally recovers missing dynamics in highly complex systems, demonstrating that the combination of efficient temporal encoding and physics-informed correction enables robust data assimilation.

cs.LG↗

arXiv2025

Accelerating scientific discovery with the common task framework

Machine learning (ML) and artificial intelligence (AI) algorithms are transforming and empowering the characterization and control of dynamic systems in the engineering, physical, and biological sciences. These emerging modeling paradigms require comparative metrics to evaluate a diverse set of scientific objectives, including forecasting, state reconstruction, generalization, and control, while also considering limited data scenarios and noisy measurements. We introduce a common task framework (CTF) for science and engineering, which features a growing collection of challenge data sets with a diverse set of practical and common objectives. The CTF is a critically enabling technology that has contributed to the rapid advance of ML/AI algorithms in traditional applications such as speech recognition, language processing, and computer vision. There is a critical need for the objective metrics of a CTF to compare the diverse algorithms being rapidly developed and deployed in practice today across science and engineering.

cs.LG↗