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Learning nonparametric systems of Ordinary Differential Equations (ODEs) $$\dot x = f(t,x)$$ from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for $$f$$ for which the solution of the ODE exists and is unique. Learning $$f$$ consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the $L^2$ distance between $$x$$ and its estimator. Experiments are provided for the FitzHugh–Nagumo oscillator, the Lorenz system, and for predicting the Amyloid level in the cortex of aging subjects. In all cases, we show competitive results compared with the state-of-the-art. 

Abstract Digital light processing bioprinting favors biofabrication of tissues with improved structural complexity. However, soft-tissue fabrication with this method remains a challenge to balance the physical performances of the bioinks for high-fidelity bioprinting and suitable microenvironments for the encapsulated cells to thrive. Here, we propose a molecular cleavage approach, where hyaluronic acid methacrylate (HAMA) is mixed with gelatin methacryloyl to achieve high-performance bioprinting, followed by selectively enzymatic digestion of HAMA, resulting in tissue-matching mechanical properties without losing the structural complexity and fidelity. Our method allows cellular morphological and functional improvements across multiple bioprinted tissue types featuring a wide range of mechanical stiffness, from the muscles to the brain, the softest organ of the human body. This platform endows us to biofabricate mechanically precisely tunable constructs to meet the biological function requirements of target tissues, potentially paving the way for broad applications in tissue and tissue model engineering.