PhD Proposal: Differentiable Systems for Efficient Optimization: From Dynamics to Geometry

Modern scientific and engineering challenges in dynamical systems often require searching immense solution spaces. Sampling these spaces blindly is computationally prohibitive, yet many underlying processes are nearly everywhere differentiable: physical states evolve smoothly in time, and even brief discontinuities preserve overall continuity. When a system’s next state and its gradient with respect to the current state are available, these gradients act as beacons that steer optimization far more efficiently than gradient‑free exploration. Consequently, researchers are investing heavily in differentiable models of real‑world phenomena, especially within physics, where the laws of motion and interaction naturally provide the required smoothness.
In this proposal, I first demonstrate how system‑level gradients can be harnessed to accelerate policy learning by fusing them with the popular reinforcement learning algorithms, using gradient information to constrain policy updates and speed convergence. This result motivates the development of two differentiable systems at the heart of the work: (1) a GPU‑accelerated differentiable traffic simulator with vehicle‑dynamics gradients, enabling rapid optimization of traffic control and management problems; and (2) a probabilistic triangular‑mesh formulation that turns connectivity existence into a continuous variable, letting gradients flow through topological changes and yielding high‑fidelity 2D and 3D reconstructions. By weaving these case studies together, this proposal charts a unified path for integrating physics and geometry into a common, scalable, gradient‑based optimization learning framework.