One leading algorithmic paradigm on NISQ computers is theVariational Quantum Algorithm (VQA) with a few prominent examples like the Variational Quantum Eignensolver (VQE) [50], quantum approximate optimization algorithm (QAOA) [20], and more in [4]. Quantum machine learning isafast-developing emerging field (e.g., see the survey [5]) where variational quantum algorithms (VQAs) (e.g., see thesurvey[4]areoneofthemost promising candidates forNISQ applications.

We introduce JAX MD, a software package for performing differentiable physics simulations with a focus on molecular dynamics. JAX MD includes a number of statistical physics simulation environments as well as interaction potentials and neural networks that can be integrated into these environments without writing any additional code. Since the simulations themselves are differentiable functions, entire trajectories can be differentiated to perform meta-optimization. These features are built on primitive operations, such as spatial partitioning, that allow simulations to scale to hundreds-of-thousands of particles on a single GPU. These primitives are flexible enough that they can be used to scale up workloads outside of molecular dynamics.

We present a method for differentiable simulation of soft articulated bodies.

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE.

The physics solvers employed for neural network training are primarily iterative, and hence, differentiating through them introduces a severe computational burden as iterations grow large. Inspired by works in bilevel optimization, we show that full accuracy of the network is achievable through physics significantly coarser than fully converged solvers. We propose Progressively Refined Differentiable Physics (PRDP), an approach that identifies the level of physics refinement sufficient for full training accuracy. By beginning with coarse physics, adaptively refining it during training, and stopping refinement at the level adequate for training, it enables significant compute savings without sacrificing network accuracy. Our focus is on differentiating iterative linear solvers for sparsely discretized differential operators, which are fundamental to scientific computing. PRDP is applicable to both unrolled and implicit differentiation. We validate its performance on a variety of learning scenarios involving differentiable physics solvers such as inverse problems, autoregressive neural emulators, and correction-based neural-hybrid solvers. In the challenging example of emulating the Navier-Stokes equations, we reduce training time by 62%.

Differentiable simulators have recently shown great promise for training autonomous vehicle controllers. Being able to backpropagate through them, they can be placed into an end-to-end training loop where their known dynamics turn into useful priors for the policy to learn, removing the typical black box assumption of the environment. So far, these systems have only been used to train policies. However, this is not the end of the story in terms of what they can offer. Here, for the first time, we use them to train world models. Specifically, we present three new task setups that allow us to learn next state predictors, optimal planners, and optimal inverse states. Unlike analytic policy gradients (APG), which requires the gradient of the next simulator state with respect to the current actions, our proposed setups rely on the gradient of the next state with respect to the current state. We call this approach Analytic World Models (AWMs) and showcase its applications, including how to use it for planning in the Waymax simulator. Apart from pushing the limits of what is possible with such simulators, we offer an improved training recipe that increases performance on the large-scale Waymo Open Motion dataset by up to 12% compared to baselines at essentially no additional cost.