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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. 

Central nervous system (CNS) tumors come with vastly heterogeneous histologic, molecular, and radiographic landscapes, rendering their precise characterization challenging. The rapidly growing fields of biophysical modeling and radiomics have shown promise in better characterizing the molecular, spatial, and temporal heterogeneity of tumors. Integrative analysis of CNS tumors, including clinically acquired multi-parametric magnetic resonance imaging (mpMRI) and the inverse problem of calibrating biophysical models to mpMRI data, assists in identifying macroscopic quantifiable tumor patterns of invasion and proliferation, potentially leading to improved ( a) detection/segmentation of tumor subregions and ( b) computer-aided diagnostic/prognostic/predictive modeling. This article presents a summary of ( a) biophysical growth modeling and simulation,( b) inverse problems for model calibration, ( c) these models' integration with imaging workflows, and ( d) their application to clinically relevant studies. We anticipate that such quantitative integrative analysis may even be beneficial in a future revision of the World Health Organization (WHO) classification for CNS tumors, ultimately improving patient survival prospects.