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Neural operators have proven to be a promising approach for modeling spatiotemporal sys- tems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense—these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive er- ror growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather fore- casting system. We demonstrate that applying our design principles to neural operators leads to significantly lower errors for long-term forecasts as well as longer time horizons without qualitative signs of divergence compared to the original models for these systems. We open-source our code for reproducibility. 

Recently there has been upsurge in reports that illicit seizures of cocaine and heroin have been adulterated with fentanyl. Surface-enhanced Raman spectroscopy (SERS) provides a useful alternative to current screening procedures that permits detection of trace levels of fentanyl in mixtures. Samples are solubilized and allowed to interact with aggregated colloidal nanostars to produce a rapid and sensitive assay. In this study, we present the quantitative determination of fentanyl in heroin and cocaine using SERS, using a point-and-shoot handheld Raman system. Our protocol is optimized to detect pure fentanyl down to 0.20 ± 0.06 ng/mL and can also distinguish pure cocaine and heroin at ng/mL levels. Multiplex analysis of mixtures is enabled by combining SERS detection with principal component analysis and super partial least squares regression discriminate analysis (SPLS-DA), which allow for the determination of fentanyl as low as 0.05% in simulated seized heroin and 0.10% in simulated seized cocaine samples.