Ishir Rao

Andrew Bukowski, Aditya Kothari, Simba Shi et al.

A diffusion model trained on Hamiltonian trajectories can achieve rollout MSE near $10^{-3}$, but the standard deviation of its energy over time is between 7500 and 36000 times larger than the ground-truth energy standard deviation, indicating a failure to preserve conservation laws. This gap motivates our central question of whether neural networks can learn or select globally conserved quantities from physical trajectories. We investigate this across three Hamiltonian systems: projectile motion, pendulum, and spring-mass. We use a structured $T(v)+V(q)$ energy model, a black-box Conservation Discovery Network (CDN), a polynomial CDN, and a conditional diffusion baseline. The structured network reaches $R^2 \geq 0.9999$ against analytical energy on clean data, while the black-box CDN reaches $R^2 \geq 0.996$ when trained with temporal consistency plus a small alignment loss to analytical energy at $t=0$ ($λ_{\mathrm{align}}=0.2$). With $λ_{\mathrm{align}}=0$, CDN Pearson $R^2$ collapses on pendulum and spring-mass ($< 10^{-3}$), showing that temporal consistency alone is not enough to reliably identify the true energy. Under $1\%$ additive Gaussian noise, the CDN outperforms the structured model on the projectile and spring-mass systems, suggesting that the CDN may be more robust to noisy inputs in this setting. However, the polynomial CDN is sensitive to training configuration: it achieves $R^2=0.78$ under a short training schedule on the pendulum system, but reaches $R^2=0.9998$ with more training time and data, regardless of whether noise is added.

Ishir Rao

Pandemics involve the high transmission of a disease that impacts global and local health and economic patterns. The impact of a pandemic can be minimized by enforcing certain restrictions on a community. However, while minimizing infection and death rates, these restrictions can also lead to economic crises. Epidemiological models help propose pandemic control strategies based on non-pharmaceutical interventions such as social distancing, curfews, and lockdowns, reducing the economic impact of these restrictions. However, designing manual control strategies while considering disease spread and economic status is non-trivial. Optimal strategies can be designed through multi-objective reinforcement learning (MORL) models, which demonstrate how restrictions can be used to optimize the outcome of a pandemic. In this research, we utilized an epidemiological Susceptible, Exposed, Infected, Recovered, Deceased (SEIRD) model: a compartmental model for virtually simulating a pandemic day by day. We combined the SEIRD model with a deep double recurrent Q-network to train a reinforcement learning agent to enforce the optimal restriction on the SEIRD simulation based on a reward function. We tested two agents with unique reward functions and pandemic goals to obtain two strategies. The first agent placed long lockdowns to reduce the initial spread of the disease, followed by cyclical and shorter lockdowns to mitigate the resurgence of the disease. The second agent provided similar infection rates but an improved economy by implementing a 10-day lockdown and 20-day no-restriction cycle. This use of reinforcement learning and epidemiological modeling allowed for both economic and infection mitigation in multiple pandemic scenarios.