Joshua L. Proctor

Zhe Bai, Eurika Kaiser, Joshua L. Proctor et al.

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, we integrate and unify two recent innovations that extend DMD to systems with actuation [Proctor et al., 2016] and systems with heavily subsampled measurements [Brunton et al., 2015]. When combined, these methods yield a novel framework for compressive system identification [code is publicly available at: https://github.com/zhbai/cDMDc]. It is possible to identify a low-order model from limited input-output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data is available, it is possible to dramatically accelerate downstream computations by first compressing the data. We demonstrate this unified framework on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, we explore this architecture on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test-case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.

Katherine A. Rosenfeld, Maike Sonnewald, Sonia J. Jindal et al.

We introduce a framework for the use of large language models (LLMs) in Building Understandable Messaging for Policy and Evidence Review (BUMPER). LLMs are proving capable of providing interfaces for understanding and synthesizing large databases of diverse media. This presents an exciting opportunity to supercharge the translation of scientific evidence into policy and action, thereby improving livelihoods around the world. However, these models also pose challenges related to access, trust-worthiness, and accountability. The BUMPER framework is built atop a scientific knowledge base (e.g., documentation, code, survey data) by the same scientists (e.g., individual contributor, lab, consortium). We focus on a solution that builds trustworthiness through transparency, scope-limiting, explicit-checks, and uncertainty measures. LLMs are rapidly being adopted and consequences are poorly understood. The framework addresses open questions regarding the reliability of LLMs and their use in high-stakes applications. We provide a worked example in health policy for a model designed to inform measles control programs. We argue that this framework can facilitate accessibility of and confidence in scientific evidence for policymakers, drive a focus on policy-relevance and translatability for researchers, and ultimately increase and accelerate the impact of scientific knowledge used for policy decisions.

B. W. Brunton, S. L. Brunton, J. L. Proctor et al.

The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude sparser still. We define enhanced sparsity as the reduction in number of measurements required for classification over reconstruction. In this work, we exploit enhanced sparsity and learn spatial sensor locations that optimally inform a categorical decision. The algorithm solves an l1-minimization to find the fewest entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space. Once the sensor locations have been identified from the training data, subsequent test samples are classified with remarkable efficiency, achieving performance comparable to that obtained by discrimination using the full image. Sensor locations may be learned from full images, or from a random subsample of pixels. For classification between more than two categories, we introduce a coupling parameter whose value tunes the number of sensors selected, trading accuracy for economy. We demonstrate the algorithm on example datasets from image recognition using PCA for feature extraction and LDA for discrimination; however, the method can be broadly applied to non-image data and adapted to work with other methods for feature extraction and discrimination.