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Abstract Fish fin rays constitute a sophisticated control system for ray-finned fish, facilitating versatile locomotion within complex fluid environments. Despite extensive research on the kinematics and hydrodynamics of fish locomotion, the intricate control strategies in fin-ray actuation remain largely unexplored. While deep reinforcement learning (DRL) has demonstrated potential in managing complex nonlinear dynamics; its trial-and-error nature limits its application to problems involving computationally demanding environmental interactions. This study introduces a cutting-edge off-policy DRL algorithm, interacting with a fluid–structure interaction (FSI) environment to acquire intricate fin-ray control strategies tailored for various propulsive performance objectives. To enhance training efficiency and enable scalable parallelism, an innovative asynchronous parallel training (APT) strategy is proposed, which fully decouples FSI environment interactions and policy/value network optimization. The results demonstrated the success of the proposed method in discovering optimal complex policies for fin-ray actuation control, resulting in a superior propulsive performance compared to the optimal sinusoidal actuation function identified through a parametric grid search. The merit and effectiveness of the APT approach are also showcased through comprehensive comparison with conventional DRL training strategies in numerical experiments of controlling nonlinear dynamics. 

Abstract Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations. 

Abstract Tissue dynamics play critical roles in many physiological functions and provide important metrics for clinical diagnosis. Capturing real-time high-resolution 3D images of tissue dynamics, however, remains a challenge. This study presents a hybrid physics-informed neural network algorithm that infers 3D flow-induced tissue dynamics and other physical quantities from sparse 2D images. The algorithm combines a recurrent neural network model of soft tissue with a differentiable fluid solver, leveraging prior knowledge in solid mechanics to project the governing equation on a discrete eigen space. The algorithm uses a Long-short-term memory-based recurrent encoder-decoder connected with a fully connected neural network to capture the temporal dependence of flow-structure-interaction. The effectiveness and merit of the proposed algorithm is demonstrated on synthetic data from a canine vocal fold model and experimental data from excised pigeon syringes. The results showed that the algorithm accurately reconstructs 3D vocal dynamics, aerodynamics, and acoustics from sparse 2D vibration profiles. 

Model-based reinforcement learning (MBRL) is believed to have much higher sample efficiency compared with model-free algorithms by learning a predictive model of the environment. However, the performance of MBRL highly relies on the quality of the learned model, which is usually built in a black-box manner and may have poor predictive accuracy outside of the data distribution. The deficiencies of the learned model may prevent the policy from being fully optimized. Although some uncertainty analysis-based remedies have been proposed to alleviate this issue, model bias still poses a great challenge for MBRL. In this work, we propose to leverage the prior knowledge of underlying physics of the environment, where the governing laws are (partially) known. In particular, we developed a physics-informed MBRL framework, where governing equations and physical constraints are used to inform the model learning and policy search. By incorporating the prior information of the environment, the quality of the learned model can be notably improved, while the required interactions with the environment are significantly reduced, leading to better sample efficiency and learning performance. The effectiveness and merit have been demonstrated over a handful of classic control problems, where the environments are governed by canonical ordinary/partial differential equations.