This manuscript presents a complete framework for the development and verification of physics-informed neural networks with application to the alternating-current power flow (ACPF) equations. Physics-informed neural networks (PINN)s have received considerable interest within power systems communities for their ability to harness underlying physical equations to produce simple neural network architectures that achieve high accuracy using limited training data. The methodology developed in this work builds on existing methods and explores new important aspects around the implementation of PINNs including: (i) obtaining operationally relevant training data, (ii) efficiently training PINNs and using pruning techniques to reduce their complexity, and (iii) globally verifying the worst-case predictions given known physical constraints. The methodology is applied to the IEEE-14 and 118 bus systems where PINNs show substantially improved accuracy in a data-limited setting and attain better guarantees with respect to worst-case predictions.
Sustainable aviation fuels (SAFs) offer an effective pathway to decarbonize the aviation sector, which accounts for about 5% of the global net effective radiative forcing, and is expected to double in the next two decades. A primary objective of the SAF GC Roadmap is to develop sustainable fuels that avoid “sooting, aerosols, and other contributors to vapor trail emissions." Another parts of this project is motivated by ongoing efforts to develop aromatic-free SAFs by using cycloalkanes to match seal swell characteristics of current fossil-based jet fuel (e.g. Jet A).
Monte Carlo simulations are at the heart of many high-fidelity simulations and analyses for radiation transport systems. As is the case with any complex computational model, it is important to propagate sources of input uncertainty and characterize how they affect model output. Unfortunately, uncertainty quantification (UQ) is made difficult by the stochastic variability that Monte Carlo transport solvers introduce. The standard method to avoid corrupting the UQ statistics with the transport solver noise is to increase the number of particle histories, resulting in very high computational costs. In this contribution, we propose and analyze a sampling estimator based on the law of total variance to compute UQ variance even in the presence of residual noise from Monte Carlo transport calculations. We rigorously derive the statistical properties of the new variance estimator, compare its performance to that of the standard method, and demonstrate its use on neutral particle transport model problems involving both attenuation and scattering physics. We illustrate, both analytically and numerically, the estimator's statistical performance as a function of available computational budget and the distribution of that budget between UQ samples and particle histories. We show analytically and corroborate numerically that the new estimator is unbiased, unlike the standard approach, and is more accurate and precise than the standard estimator for the same computational budget.
