Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations which resolve these systems with high accuracy. However, as these simulations incur high computational costs, they are infeasible to be employed for large-scale analysis. A popular alternative to simulators are neural network surrogates which are trained in a data-driven manner and are much more computationally efficient. However, these surrogate models suffer from high rollout error when used autoregressively, especially when confronted with training data paucity. Existing work proposes to improve surrogate rollout error by either including physical loss terms directly in the optimization of the model or incorporating computational simulators as'differentiable layers' in the neural network. Both of these approaches have their challenges, with physical loss functions suffering from slow convergence for stiff PDEs and simulator layers requiring gradients which are not always available, especially in legacy simulators. We propose the Hybrid PDE Predictor with Reinforcement Learning (HyPER) model: a modelagnostic, RL based, cost-aware model which combines a neural surrogate, RL decision model, and a physics simulator (with or without gradients) to reduce surrogate rollout error significantly. In addition to reducing in-distribution rollout error by 47%-78%, HyPER learns an intelligent policy that is adaptable to changing physical conditions and resistant to noise corruption. Scientific simulations have been the workhorse enabling novel discoveries across many scientific disciplines. However, executing fine-grained simulations of a scientific process of interest is a costly undertaking requiring large computational resources and long execution times.

Using observational data to learn causal relationships is essential when randomized experiments are not possible, such as in healthcare. Discovering causal relationships in time-series health data is even more challenging when relationships change over the course of a disease, such as medications that are most effective early on or for individuals with severe disease. Stage variables such as weeks of pregnancy, disease stages, or biomarkers like HbA1c, can influence what causal relationships are true for a patient. However, causal inference within each stage is often not possible due to limited amounts of data, and combining all data risks incorrect or missed inferences. To address this, we propose Causal Discovery with Stage Variables (CDSV), which uses stage variables to reweight data from multiple time-series while accounting for different causal relationships in each stage. In simulated data, CDSV discovers more causes with fewer false discoveries compared to baselines, in eICU it has a lower FDR than baselines, and in MIMIC-III it discovers more clinically relevant causes of high blood pressure.