Utkarsh Utkarsh

Sharv Murgai, Utkarsh Utkarsh, Kyle C. Nguyen et al.

Agent-based epidemic models (ABMs) encode behavioral and policy heterogeneity but are too slow for nightly hospital planning. We develop county-ready surrogates that learn directly from exascale ABM trajectories using Universal Differential Equations (UDEs): mechanistic SEIR-family ODEs with a neural-parameterized contact rate $κ_φ(u,t)$ (no additive residual). Our contributions are threefold: we adapt multiple shooting and an observer-based prediction-error method (PEM) to stabilize identification of neural-augmented epidemiological dynamics across intervention-driven regime shifts; we enforce positivity and mass conservation and show the learned contact-rate parameterization yields a well-posed vector field; and we quantify accuracy, calibration, and compute against ABM ensembles and UDE baselines. On a representative ExaEpi scenario, PEM-UDE reduces mean MSE by 77% relative to single-shooting UDE (3.00 vs. 13.14) and by 20% relative to MS-UDE (3.75). Reliability improves in parallel: empirical coverage of ABM $10$-$90$% and $25$-$75$% bands rises from 0.68/0.43 (UDE) and 0.79/0.55 (MS-UDE) to 0.86/0.61 with PEM-UDE and 0.94/0.69 with MS+PEM-UDE, indicating calibrated uncertainty rather than overconfident fits. Inference runs in seconds on commodity CPUs (20-35 s per $\sim$90-day forecast), enabling nightly ''what-if'' sweeps on a laptop. Relative to a $\sim$100 CPU-hour ABM reference run, this yields $\sim10^{4}\times$ lower wall-clock per scenario. This closes the realism-cadence gap, supports threshold-aware decision-making (e.g., maintaining ICU occupancy $<75$%), preserves mechanistic interpretability, and enables calibrated, risk-aware scenario planning on standard institutional hardware. Beyond epidemics, the ABM$\to$UDE recipe provides a portable path to distill agent-based simulators into fast, trustworthy surrogates for other scientific domains.

Utkarsh Utkarsh, Pengfei Cai, Alan Edelman et al.

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies, remains challenging. Existing methods often rely on soft penalties or architectural biases that fail to guarantee hard constraints. In this work, we propose Physics-Constrained Flow Matching (PCFM), a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models. PCFM continuously guides the sampling process through physics-based corrections applied to intermediate solution states, while remaining aligned with the learned flow and satisfying physical constraints. Empirically, PCFM outperforms both unconstrained and constrained baselines on a range of PDEs, including those with shocks, discontinuities, and sharp features, while ensuring exact constraint satisfaction at the final solution. Our method provides a general framework for enforcing hard constraints in both scientific and general-purpose generative models, especially in applications where constraint satisfaction is essential.

Utkarsh Utkarsh, Danielle C. Maddix, Ruijun Ma et al.

We present ProbHardE2E, a probabilistic forecasting framework that incorporates hard operational/physical constraints, and provides uncertainty quantification. Our methodology uses a novel differentiable probabilistic projection layer (DPPL) that can be combined with a wide range of neural network architectures. DPPL allows the model to learn the system in an end-to-end manner, compared to other approaches where constraints are satisfied either through a post-processing step or at inference. ProbHardE2E optimizes a strictly proper scoring rule, without making any distributional assumptions on the target, which enables it to obtain robust distributional estimates (in contrast to existing approaches that generally optimize likelihood-based objectives, which are heavily biased by their distributional assumptions and model choices); and it can incorporate a range of non-linear constraints (increasing the power of modeling and flexibility). We apply ProbHardE2E in learning partial differential equations with uncertainty estimates and to probabilistic time-series forecasting, showcasing it as a broadly applicable general framework that connects these seemingly disparate domains.