Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably sa...
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Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably sa...
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The Koopman operator has recently garnered much attention for its value in dynamicalsystems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of exte...
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ISBN:
(纸本)9781538679012;9781538679265
The Koopman operator has recently garnered much attention for its value in dynamicalsystems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition;this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a computational framework for learning Koopman operators of nonlinear dynamicalsystems using deep learning. We show that this novel method automatically selects efficient deep dictionaries, requiring much lower dimensional dictionaries while outperforming state-of-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict on test data quantitatively 100 steps into the future, using only a single timepoint as an initial condition, and quantitative oscillatory behavior 400 steps into the future.
Diffusion-weighted MRI (DWI) is essential for stroke diagnosis, treatment decisions, and prognosis. However, image and disease variability hinder the development of generalizable AI algorithms with clinical value. We ...
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Diffusion-weighted MRI (DWI) is essential for stroke diagnosis, treatment decisions, and prognosis. However, image and disease variability hinder the development of generalizable AI algorithms with clinical value. We address this gap by presenting a novel ensemble algorithm derived from the 2022 Ischemic Stroke Lesion Segmentation (ISLES) challenge. ISLES’22 provided 400 patient scans with ischemic stroke from various medical centers, facilitating the development of a wide range of cutting-edge segmentation algorithms by the research community. By assessing them against a hidden test set, we identified strengths, weaknesses, and potential biases. Through collaboration with leading teams, we combined top-performing algorithms into an ensemble model that overcomes the limitations of individual solutions. Our ensemble model combines the individual algorithms’ strengths and achieved superior ischemic lesion detection and segmentation accuracy (median Dice score: 0.82, median lesion-wise F1 score: 0.86) on our internal test set compared to individual algorithms. This accuracy generalized well across diverse image and disease variables. Furthermore, the model excelled in extracting clinical biomarkers like lesion types and affected vascular territories. Notably, in a Turing-like test, neuroradiologists consistently preferred the algorithm’s segmentations over manual expert efforts, highlighting increased comprehensiveness and precision. Validation using a real-world external dataset (N=1686) confirmed the model’s generalizability (median Dice score: 0.82, median lesion-wise F1 score: 0.86). The algorithm’s outputs also demonstrated strong correlations with clinical scores (admission NIHSS and 90-day mRS) on par with or exceeding expert-derived results, underlining its clinical relevance. This study offers two key findings. First, we present an ensemble algorithm that detects and segments ischemic stroke lesions on DWI across diverse scenarios on par with expert (neuro)rad
Andy Packard, an expert from University of California at Berkeley (UCB) Mechanical Engineering Department shares views on the use of sum-of-squares (SOS) methods to determine the region of attraction (ROA). SOS applie...
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Andy Packard, an expert from University of California at Berkeley (UCB) Mechanical Engineering Department shares views on the use of sum-of-squares (SOS) methods to determine the region of attraction (ROA). SOS applies to polynomials in several real variables and a polynomial is a finite linear combination of monomials. The ROA can be visualized by simulating the system from many initial conditions and plotting the trajectories in a phase plane plot for systems with two or three states. SOS techniques can be used to perform nonlinear analyses, including computation of input/output gains, estimation of reachable sets, and computation of robustness margins. The approaches that apply to SOS methods includes the computational requirements that grow rapidly in the number of variables and polynomial degree, which roughly limits SOS-based analysis to systems with at most eight to ten states, one to two inputs, and polynomial vector fields of degree 3.
In this issue of IEEE controlsystems Magazine, Andy Packard and friends respond to a query on determining the region of attraction using sum-of-squares methods.
In this issue of IEEE controlsystems Magazine, Andy Packard and friends respond to a query on determining the region of attraction using sum-of-squares methods.
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