200 dimensions of complex physical motion can now be solved in less than 30 minutes.
April 24, 2026
Original Paper
Tropical low-rank approximation and application to optimal control of N-body systems
arXiv · 2604.18785
The Takeaway
Calculating the optimal control for a system with hundreds of interacting parts is typically a computational nightmare. This new method uses tropical low-rank approximation to simplify the math without losing accuracy. It allows engineers to compute value functions for N-body systems that were previously impossible to handle. The speed of the calculation makes it feasible to run these simulations on standard hardware. This technology opens up new possibilities for controlling everything from drone swarms to complex chemical reactions.
From the abstract
We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by \(N\)-body systems. In this setting, the action functional consists of local kinetic and potential terms, along with an interaction potential. We exploit this structure to approximate the value function using a tropical tensor of small rank, i.e.\ a supremum of a small number of additively separable functions. We propose a trajectory-based tropical low-rank approximat