耶鲁大学

Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning. Despite this promise, how to train PINOs efficiently and robustly remains less well-understood than the training of either data-driven neural operators or physics-informed neural networks (PINNs). To bridge this gap, we examine key components of the PINO training pipeline, including architecture design, optimizer choice, loss balancing, and collocation-point sampling strategy. We study three representative operator backbones, Deep Operator Network (DeepONet), Fourier Neural Operator (FNO), and Continuous Vision Transformer (CViT), across five diverse parametric PDE systems. Our results show that CViT provides consistently strong and stable performance across the considered benchmarks. Beyond architecture, we find that several optimization pathologies previously identified in PINN training naturally arise in PINOs, including gradient conflicts and causal violation. We also find that mitigation algorithms developed for PINNs remain effective in the PINO setting. We further compare physics-informed and data-driven training under different data regimes, revealing that a carefully designed physics-informed training pipeline can match, and in some cases, outperform purely data-driven neural operators. Taken together, these findings provide a systematic empirical understanding of the optimization challenges in PINO training and inform a practical pipeline for efficient and robust physics-informed operator learning. Code and data are available at https://github.com/NanxiiChen/PI-CViT.

The Freshwater Lake model (FLake) has recently been integrated into the land surface scheme of ERA5 and subsequently downscaled to ERA5-Land, enabling the investigation of global-scale lake thermodynamics at an enhanced spatial resolution. Although ERA5-Land's capability in simulating lake surface water temperature (Ts) has been recognized, its performance in reproducing other critical lake variables remains inadequately explored. This study comprehensively evaluated ERA5-Land atmospheric forcings and lake products against long-term observations at Lake Taihu, a large, subtropical shallow lake. Results show that ERA5-Land captures the surface microclimates reasonably well at Lake Taihu across diurnal to annual scales. Satisfactory performance is also achieved in simulating monthly and annual latent heat fluxes (7E) with a positive bias of 1.0 W m- 2 (or 1% of the annual mean). However, water stratification simulated by ERA5-Land is excessively strong in spring and summer. ERA5-Land systematically overestimates downward shortwave radiation (+16 W m- 2) and underestimates downward longwave radiation (-13 W m- 2) due to cloud cover underestimation. These intrinsic radiative biases only introduce a marginal error in simulated Ts and 7E due to the compensation effect between downward shortwave and longwave components. Our proposed correction algorithm can reduce monthly radiative biases both for an independent period at Lake Taihu and at geographically independent Poyang Lake. Notably, despite lacking lake-specific parameter optimization, the default ERA5-Land configuration still outperforms two other FLake simulations using satellite-calibrated parameters in reproducing the multi-year mean Ts. Furthermore, Flake model in ERA5-Land simulates an identical lake warming trend (0.26 degrees C decade- 1 from 1981 to 2020) and a comparable evaporation changing rate (2.9 W m- 2 decade- 1 from 1979 to 2013) to other independent simulations with tuned parameters, highlighting its reliability for investigating long-term trends in lake thermodynamics.

High-grade dysplastic nodules (HGDN) are recognized precursors of hepatocellular carcinoma in cirrhosis, yet their distinction from macro-regenerative nodules (MRN) relies entirely on morphologic features that exist along a continuum rather than as discrete thresholds, with no ancillary marker available to adjudicate this boundary. Whether these lesions represent distinct molecular states remains unknown. We performed whole-transcriptome spatial profiling (GeoMx Digital Spatial Profiler, Bruker) of MRN and HGDN within their native cirrhotic microenvironment in FFPE explant specimens from three patients. Fifteen regions of interest spanning background cirrhosis (n = 2), MRN (n = 3), HGDN (n = 4), and the HGDN–cirrhotic interface (n = 6) underwent exploratory differential expression and gene set enrichment analyses; because MRN and HGDN derived from different patients, lesion class and donor could not be separated. MRN showed a quiescent regenerative program characterized by HGFAC upregulation, depletion of inflammatory and immunoglobulin transcripts, and no significant upregulation of canonical hepatocellular carcinoma markers. HGDN showed PZP, DEPP1, and CDHR5 upregulation and enrichment of interferon signaling. Spatially, HGDN separated into a metallothionein-enriched core and an MHC-I/interferon-enriched interface expressing HLA-B, HLA-C, and IFI6, a pattern that bulk profiling would be expected to obscure; the core–interface distinction persisted when analysis was restricted to a single patient. In this pilot cohort, morphologically defined regenerative and premalignant hepatocellular nodules showed distinct transcriptional profiles, providing preliminary, hypothesis-generating molecular support for a difficult morphologic distinction. These observations, including the MHC-I/interferon-enriched dysplastic interface, identify candidate targets for validation in larger cohorts with paired lesions.

Background Allergic skin reactions induce pronounced microvascular changes that are typically evaluated using wheal-and-flare responses. While photoplethysmography imaging (PPGI) can quantify perfusion amplitude, little is known about how local inflammation affects the temporal organization of pulsatile microvascular signals. Methods This study is based on a secondary, cross-sectional observational analysis of data acquired during a previous clinical skin prick testing (SPT) protocol. Forearm PPGI recordings were acquired using a monochromatic camera, with simultaneously recorded fingertip photoplethysmography serving as a systemic reference. Cardiac-frequency components were extracted using wavelet ridge reconstruction, and phase shift (Δϕ), phase locking value (PLV), and phase-derived temporal offset (Δt) were computed. Linear mixed-effects models were used to assess associations with allergic reactivity. Results Reactive SPT sites showed increased cardiac-band perfusion and a consistent phase advance relative to both references. Allergic sites exhibited phase shifts of approximately − 0.54 rad (fingertip) and − 0.52 rad (saline), corresponding to a temporal advance of about 60–65 ms, while synchronization remained high (PLV ≈ 0.81–0.91). Conclusion Allergic inflammation is associated with local phase and temporal advance of pulsatile microvascular signals, indicating locally modified pulsatile dynamics in the skin. Phase analysis of PPGI provides complementary information beyond perfusion amplitude and may enhance objective assessment of inflammatory skin responses.

We introduce an O(M) algorithm for evaluating the azimuthal Fourier modes Gk,m , m=0,…,M , of the three-dimensional Helmholtz Green’s function with real wavenumber k , together with all their first- and second-order derivatives with respect to the cylindrical source and target coordinates. The cost is independent of both the wavenumber and the source-target separation, and high relative accuracy is retained even for modes whose magnitude is exponentially small. The method combines contour deformation at a few boundary modes with a boundary-value formulation of the five-term recurrence in the mode index. Derivative quantities are obtained from stable recurrences, adding only a small constant factor to the cost of Gk,m alone. Numerical experiments demonstrate high relative accuracy, linear scaling in M, and applications to modal boundary integral equation solvers for axisymmetric acoustic scattering, where the k-independent kernel evaluator makes dense per-mode linear algebra the dominant cost.