About

Our group develops mathematical and computational algorithms for data-driven modeling, sparse sensing, and system identification in high-dimensional dynamical systems. Drawing on physics-informed structure, statistical mechanics and spectral methods, we provide performance guarantees, interpretability, and uncertainty quantification for learned models.

Research topics

• Computer science
• Artificial intelligence
• Mathematics
• Algorithm
• Mathematical optimization

Selected publications

• OpenReservoirComputing: GPU-Accelerated Reservoir Computing in JAX

  arXiv (Cornell University) · 2026-03-16

  preprintOpen accessSenior author

  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.

  PublisherDOI

• Reservoir computing for system identification and model predictive control

  Neural Networks · 2026-05-09

  articleOpen accessSenior author

  Model predictive control (MPC), widely used for real-time control of complex dynamical systems, operates by repeatedly solving an optimization problem over a receding time horizon. Its success hinges on dynamical models that are accurate yet efficient enough for rapid online computation. Frequently, the governing models of complex systems are either unknown or computationally inefficient, forcing MPC to rely on data-driven surrogate models. Echo state networks (ESNs), a class of recurrent neural networks trained through computationally efficient ridge regression, are well-suited for this role and have demonstrated strong forecasting capabilities in chaotic dynamical systems. Their architecture naturally supports rapid training and flexible adaptation to varying control inputs. In this work, we demonstrate that ESNs serve as effective data-driven surrogates for system dynamics under diverse control scenarios, outperforming competing architectures such as long short-term memory (LSTM) networks. On challenging control benchmarks, including the Lorenz system with control and fluid flow past a cylinder, MPC with ESN surrogates consistently achieves the control objective, whereas the next-best considered architecture, LSTM-based MPC, frequently fails. Even in cases where LSTM-based MPC succeeds, ESN-based MPC reduces average control cost by up to 10% and decreases variability by as much as 85%. Beyond performance, ESNs are significantly more sample-efficient and train over an order of magnitude faster than LSTMs. These results establish ESNs as accurate, efficient architectures for scalable data-driven MPC in complex systems with limited training data and unknown dynamics.

  PublisherDOI

• Machine Learning‐Assisted Inverse Design of Soft and Multifunctional Hybrid Liquid Metal Composites

  Advanced Functional Materials · 2026-05-11

  article

  ABSTRACT Soft functional materials are essential for wearables and stretchable electronics to meet multiple performance demands. Hybrid filler composites (HFCs) with liquid and solid inclusions offer tailored properties. However, identifying optimal compositions through conventional trial‐and‐error is costly, inefficient, and generates substantial material waste. We present an inverse design framework for hybrid liquid metal composites that combines data generation from a physics‐based homogenization model with machine learning (ML) algorithms and Bayesian optimization to enable intelligent design of experiments. This framework explores ∼690 000 composite formulations across diverse polymers and solid fillers, revealing key composition–property relationships while achieving targeted optimization of thermal conductivity, elasticity, and density with minimal material use. Comparative studies between Random Forest regression and a generative model provide practical strategies for identifying synthesizable composites. An inversely designed HFC achieves a thermal conductivity of ∼2.4 W/(m·K), 1.6 × that of the liquid‐metal composite and 12 × that of the polymer, while maintaining low‐modulus, high‐strain mechanics (0.93 MPa, 155% strain) at reduced cost. Integration into flexible electronics and thermoelectrics demonstrates enhanced thermal management and energy harvesting. This work establishes a practical, ML‐assisted inverse design paradigm for guiding the discovery of multifunctional composites, readily extendable to other material systems and properties.

  PublisherDOI

• OpenReservoirComputing: GPU-Accelerated Reservoir Computing in JAX

  arXiv (Cornell University) · 2026-03-16

  articleOpen accessSenior author

  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.

  PublisherOA PDF

• Data-Enabled Stochastic Iterative Shape Control for Assembly of Flexible Structures

  ASME Letters in Dynamic Systems and Control · 2025-08-22

  article

  Abstract Joining flexible structures such as in the assembly of fuselage sections in an aircraft and on-orbit assembly of modular space structures requires precise shape matching at the joint interface to avoid large local stresses that can lead to joint failure. However, it is difficult to accurately determine the forces needed (using analytical or numerical methods) for correcting the shape variations caused during the manufacturing process. Current assembly approaches use shims to reduce stresses in the presence of shape differences between the structures being joined. In contrast, the main contribution of this work is a data-based approach to experimentally reshape flexible structures to a desired shape. Specifically, data are used to develop predictive models that are then used to iteratively control the shape of those structures using a limited number of fixed actuators. The iterative control method accounts for uncertainties in the data-enabled predictive models and noise from the system to reshape the structure accurately. Experimental results with a relatively large (about 3.3 m long) structure demonstrate that the proposed approach accurately reshapes the structure with a substantial order-of-magnitude reduction (89%) in the maximum shape error, reducing the maximum shape error from 1.19×10−2 m to 1.27×10−3 m over the length of the structure.

  PublisherDOI

• Online Kernel Dynamic Mode Decomposition for Streaming Time Series Forecasting with Adaptive Windowing

  ArXiv.org · 2025-10-17

  preprintOpen access

  Real-time forecasting from streaming data poses critical challenges: handling non-stationary dynamics, operating under strict computational limits, and adapting rapidly without catastrophic forgetting. However, many existing approaches face trade-offs between accuracy, adaptability, and efficiency, particularly when deployed in constrained computing environments. We introduce WORK-DMD (Windowed Online Random Kernel Dynamic Mode Decomposition), a method that combines Random Fourier Features with online Dynamic Mode Decomposition to capture nonlinear dynamics through explicit feature mapping, while preserving fixed computational cost and competitive predictive accuracy across evolving data. WORK-DMD employs Sherman-Morrison updates within rolling windows, enabling continuous adaptation to evolving dynamics from only current data, eliminating the need for lengthy training or large storage requirements for historical data. Experiments on benchmark datasets across several domains show that WORK-DMD achieves higher accuracy than several state-of-the-art online forecasting methods, while requiring only a single pass through the data and demonstrating particularly strong performance in short-term forecasting. Our results show that combining kernel evaluations with adaptive matrix updates achieves strong predictive performance with minimal data requirements. This sample efficiency offers a practical alternative to deep learning for streaming forecasting applications.

  PublisherOA PDFDOI

• Extending the trapping theorem to provide local stability guarantees for quadratically nonlinear models

  Physics of Fluids · 2025-10-01 · 1 citations

  article

  The Navier–Stokes equations are partial differential equations to describe the nonlinear convective motion of fluids and they are computationally expensive to simulate because of their high nonlinearity and variables being fully coupled. Reduced-order models (ROMs) are simpler models for evolving the flows by capturing only the dominant behaviors of a system and can be used to design controllers for high-dimensional systems. However it is challenging to guarantee the stability of these models either globally or locally. Ensuring the stability of ROMs can improve the interpretability of the behavior of the dynamics and help develop effective system control strategies. For quadratically nonlinear systems that represent many fluid flows, the Schlegel and Noack trapping theorem [Schlegel and Noack, “On long-term boundedness of Galerkin models,” J. Fluid Mech. 765, 325–352 (2015)] can be used to check if ROMs are globally stable (long-term bounded). This theorem was subsequently incorporated into system identification techniques that determine models directly from data [Kaptanoglu et al., “Promoting global stability in data-driven models of quadratic nonlinear dynamics,” Phys. Rev. Fluids 6, 094401 (2021)]. While the Schlegel and Noack trapping theorem provides global stability criteria for systems with strictly energy-preserving nonlinearities, many physical systems, including those with inflow/outflow boundary conditions, exhibit weakly relaxed energy-preserving structures. This work introduces two key advances: (1) a theorem establishing analytical stability bounds for linear-quadratic systems under relaxed energy-preserving constraints, explicitly quantifying the local stability radius, and (2) the extended trapping SINDy algorithm, which embeds these theoretical guarantees into data-driven system identification. By integrating Lyapunov's direct method with the trapping theorem framework, our approach enables the first provably locally stable models for quadratic dynamics with weakly broken energy-preserving nonlinearities. Several examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm.

  PublisherDOI

• Deep Learning Network-Based Fruit Name Recognition for Interactive Fruit Shopping Interface and Fruit Sugar Recommendation App

  2025-06-26

  article1st authorCorresponding

  This paper presents an deep learning approach for fruit recognition to enhance accuracy and computational efficiency for real-world applications. Fruit recognition is challenging due to variations in background, illumination and color, high processing latency, large model sizes, and the need for effective classification across multiple categories. To address these issues, the method integrates discrete cosine transform (DCT), discrete wavelet transform (DWT), and compressed imaging techniques with convolutional neural networks (CNNs) to improve feature extraction, reduce dimensionality, and enhance model robustness. The models were evaluated using the fruits 360 dataset, consisting of 141 fruit categories, and benchmarked using accuracy, precision, recall, and f1-score. Results show that the wavelet transform-based model achieved an accuracy of 97.53%, while the baseline CNN reached an accuracy of 98.05% (existing model), but with higher computational complexity. The approach improves noise resilience and reduces computational demands without significant accuracy loss. Additionally, the models were deployed in an Android application for real-time fruit recognition, demonstrating their efficiency in resource-constrained environments. This study highlights the effectiveness of integrating image processing techniques with deep learning for efficient and scalable fruit recognition, enabling applications in automated retail, precision agriculture, and dietary management.

  PublisherDOI

• Effective thermal conductivity and elastic modulus of elastomer composites with liquid metal and solid inclusions

  Composites Science and Technology · 2025-06-06 · 9 citations

  article
  PublisherDOI

• Data-driven ergonomic risk assessment of complex hand-intensive manufacturing processes

  Communications Engineering · 2025-03-12 · 6 citations

  articleOpen accessSenior author

  Hand-intensive manufacturing processes, such as composite layup and textile draping, require significant human dexterity to accommodate task complexity. These strenuous hand motions often lead to musculoskeletal disorders and rehabilitation surgeries. Here we develop a data-driven ergonomic risk assessment system focused on hand and finger activity to better identify and address these risks in manufacturing. This system integrates a multi-modal sensor testbed that captures operator upper body pose, hand pose, and applied force data during hand-intensive composite layup tasks. We introduce the Biometric Assessment of Complete Hand (BACH) ergonomic score, which measures hand and finger risks with greater granularity than existing risk scores for upper body posture (Rapid Upper Limb Assessment, or RULA) and hand activity level (HAL). Additionally, we train machine learning models that effectively predict RULA and HAL metrics for new participants, using data collected at the University of Washington in 2023. Our assessment system, therefore, provides ergonomic interpretability of manufacturing processes, enabling targeted workplace optimizations and posture corrections to improve safety.

  PublisherOA PDFDOI

Recent grants

• PostDoctoral Research Fellowship

  NSF · $150k · 2018–2022

Frequent coauthors

• Steven L. Brunton

  Dynamic Systems (United States)

  33 shared

• J. Nathan Kutz

  22 shared

• Dimitrios Giannakis

  Dartmouth College

  11 shared

• Andrew M. Stuart

  California Institute of Technology

  11 shared

• Dmitry Burov

  California Institute of Technology

  11 shared

• Bingni W. Brunton

  University of Washington

  7 shared

• J. Nathan Kutz

  5 shared

• N. Benjamin Erichson

  5 shared

Education

• Ph.D., Applied Mathematics

  University of Washington

  2018

• B.S., Mathematics and Computer Science

  University of Massachusetts Lowell

  2013