Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is required. Existing scalable AMR methods make heuristic refinement decisions based on instantaneous error estimation and thus do not aim for long-term optimality over an entire simulation. We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning (RL) to train refinement policies directly from simulation. AMR poses a new problem for RL as both the state dimension and available action set changes at every step, which we solve by proposing new policy architectures with differing generality and inductive bias. The model sizes of these policy architectures are independent of the mesh size and hence can be deployed on larger simulations than those used at train time. We demonstrate in comprehensive experiments on static function estimation and time-dependent equations that RL policies can be trained on problems without using ground truth solutions, are competitive with a widely-used error estimator, and generalize to larger, more complex, and unseen test problems. 

Traditionally, precision medicine involves classifying patients to identify subpopulations that respond favorably to specific therapeutics. We pose precision medicine as a dynamic feedback control problem, where treatment administered to a patient is guided by measurements taken during the course of treatment. We consider sepsis, a life-threatening condition in which dysregulation of the immune system causes tissue damage. We leverage an existing simulation of the innate immune response to infection and apply deep reinforcement learning (DRL) to discover an adaptive personalized treatment policy that specifies effective multicytokine therapy to simulated sepsis patients based on systemic measurements. The learned policy achieves a dramatic reduction in mortality rate over a set of 500 simulated patients relative to standalone antibiotic therapy. Advantages of our approach are threefold: (1) the use of simulation allows exploring therapeutic strategies beyond clinical practice and available data, (2) advances in DRL accommodate learning complex therapeutic strategies for complex biological systems, and (3) optimized treatments respond to a patient's individual disease progression over time, therefore, capturing both differences across patients and the inherent randomness of disease progression within a single patient. We hope that this work motivates both considering adaptive personalized multicytokine mediation therapy for sepsis and exploiting simulation with DRL for precision medicine more broadly.