arXiv subjects

Troy Yang

Publications and source records attributed to Troy Yang.

3 recordsLinked to original sources

arXiv2026

Data Assimilation with Sparse Observations

Data assimilation by nudging (also called CDA) yields exponentially decaying errors and an infinite predictability horizon if the method parameter is large enough and the observations are frequent enough in time and dense enough in space. We consider the complementary case of moderate parameters and sparse and infrequent observations. We prove that assimilation with any data and any(positive) parameter strictly decreases errors and strictly increases the (now finite) predictability horizon.

math.NA↗

arXiv2026

Higher Accuracy Modular Data Assimilation for the Navier-Stokes Equations

This paper develops an accurate and effective combination of second order backward differentiation time discretization (BDF2) with modular, 2-step nudging-based data assimilation \begin{align} \text{Forecast step: } \quad &\frac{3\widetilde{v}^{n+2}-4v^{n+1}+v^n}{2\Delta t}+\widetilde{v}^{n+2} \cdot \nabla \widetilde{v}^{n+2} - \nu \Delta \widetilde{v}^{n+2} + \nabla q^{n+2}=f(x) \notag \\ &\nabla \cdot \widetilde{v}^{n+2} = 0 \notag \\ \text{Analysis step: } \quad &\frac{3v^{n+2}-3\widetilde{v}^{n+2}}{2\Delta t}-\chi I_H(u(t^{n+2})-v^{n+2})=0. \notag \end{align} If $I_H=I_H^2$, the analysis step can be made explicit, taking the form \begin{align} v^{n+2}=\widetilde{v}^{n+2}+\frac{2\Delta t\chi}{3+2\Delta t\chi}I_H(u^{n+2}-\widetilde{v}^{n+2}). \notag \end{align} This implies the analysis step has the stability property of an implicit step and lower complexity than an explicit analysis step. Stability and error estimates for the BDF2 scheme are presented along with their proofs. Numerical experiments are conducted to assess the performance of BDF2 modular assimilation algorithm. The results of the experiments support the conclusion that modular data assimilation has comparable accuracy to standard, fully coupled data assimilation while greatly reducing computational complexity and cost.

math.NA↗

arXiv2024

Introducing the Large Medical Model: State of the art healthcare cost and risk prediction with transformers trained on patient event sequences

With U.S. healthcare spending approaching $5T (NHE Fact Sheet 2024), and 25% of it estimated to be wasteful (Waste in the US the health care system: estimated costs and potential for savings, n.d.), the need to better predict risk and optimal patient care is evermore important. This paper introduces the Large Medical Model (LMM), a generative pre-trained transformer (GPT) designed to guide and predict the broad facets of patient care and healthcare administration. The model is trained on medical event sequences from over 140M longitudinal patient claims records with a specialized vocabulary built from medical terminology systems and demonstrates a superior capability to forecast healthcare costs and identify potential risk factors. Through experimentation and validation, we showcase the LMM's proficiency in not only in cost and risk predictions, but also in discerning intricate patterns within complex medical conditions and an ability to identify novel relationships in patient care. The LMM is able to improve both cost prediction by 14.1% over the best commercial models and chronic conditions prediction by 1.9% over the best transformer models in research predicting a broad set of conditions. The LMM is a substantial advancement in healthcare analytics, offering the potential to significantly enhance risk assessment, cost management, and personalized medicine.

cs.LG↗