Snapshots of recent research

Artifacts of Numerical Integration in Learning Dynamical Systems

Paper: Research in the Mathematical Sciences 13, 66 (2026) (arXiv:2507.14491). Homepage: Project page.

When learning a dynamical system from data, the numerical integrator inside the training loop silently shapes what is learned. A damped oscillator can be confidently identified as anti-damped; a conservative predator–prey model can be learned with spurious dissipation. The key insight is that different integrators (forward Euler, RK4, implicit midpoint) have different stability regions, and the optimizer finds parameters that satisfy the discrete map — not the continuous-time ODE. The fix is to use a structure-preserving integrator whose stability region matches the left half complex plane, such as the implicit midpoint rule.

Learned Lotka-Volterra with RK4: trajectories spiraling inward due to integrator artifact — Learned Lotka–Volterra model trained with RK4. The true orbits are closed loops, but the learned vector field produces trajectories that spiral inward — a non-physical dissipation introduced entirely by the integrator.

Optimal 6G Transmitter Placement in Realistic Urban Environments

Paper: https://arxiv.org/abs/2604.28153. Homepage: Project page.

High-fidelity 3D model of San Francisco used for ray-tracing simulations.

Data rate coverage maps: AT&T baseline vs. IA-SPA optimized placement — High-fidelity 3D model of San Francisco used for ray-tracing simulations.

Metric	AT&T Baseline	IA-SPA	Change
Data Rate [Mbps]
Mean Rate	21.18	36.10	+70.4%
Edge Rate (5th pct.)	5.51	10.36	+88.0%
Interference [nW]
Mean Interference	2.24	2.19	−2.0%
Max Interference	495.86	473.93	−4.4%

Pursuit-evasion game of Reeds–Shepp cars using Deep Learning

Paper: https://arxiv.org/abs/2406.10758.

Demos: