RATIONALE AND OBJECTIVES:In clinical practice, the preoperative risk assessment of adrenal metastases versus benign adrenal lesions carries a substantial risk of misdiagnosis. The artificial intelligence technology holds promise for reducing misdiagnosis rates. However, due to the problem of data privacy protection and non-independent and identically distributed of multi-center data, the performance of artificial intelligence models is significantly affected. MATERIALS AND METHODS:We retrospectively collected 1187 adrenal lesions from 1100 patients who underwent three phase Computed tomography (CT) scanning between January 2008 and September 2021. And then, we combined graph structure networks and mutual information to construct a robust federated learning model (RFLM) for the preoperative risk assessment of adrenal metastases and adrenal benign lesions. We conducted experiments on three-phase (pre-contrast phase (PCP), venous phase (VP) and arterial phase (AP)). In addition, we also conduct correlation analysis of the features of each center in RFLM to explore the intrinsic mechanism of the model. RESULTS:PCP-based RFLM outperformed AP/VP and the evaluated federated learning baselines on all four center-specific test sets, with AUCs of 0.7826, 0.8318, 0.8794, and 0.8895 for Centers 1-4, respectively. Additional analyses supported its superior performance and potential clinical utility across centers. CONCLUSION:Our results indicate that PCP-based RFLM enables effective preoperative risk assessment of adrenal metastases and benign lesions, potentially reducing reliance on enhanced CT and thus minimizing additional radiation and complications. These findings underscore RFLM as a robust and reliable diagnostic approach.

We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecasting. Machine learning serves as an efficient numerical model for predicting dynamical systems. However, even with sufficient data, model uncertainty remains and accumulates over time, causing the long-term performance of ML models to deteriorate. To overcome this difficulty, we integrate data assimilation techniques into the training process to iteratively refine the model predictions by incorporating observational information. Specifically, we apply the Ensemble Score Filter (EnSF), a generative AI-based training-free diffusion model approach, for solving the data assimilation problem in high-dimensional nonlinear complex systems. This leads to a hybrid data assimilation-training framework that combines ML with EnSF to improve long-term predictive performance. We shall demonstrate that EnSF-enhanced ML can effectively reduce predictive uncertainty in ML-based Lorenz-96 system prediction and the Korteweg-De Vries (KdV) equation prediction.

We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under uncertainty, their practical use typically requires specifying the magnitude and structure of model uncertainties that are often unknown and difficult to infer from noisy measurements. To address this challenge, we develop a stochastic operator-learning framework that learns directly from noisy data and outputs both a mean solution field and a quantification of uncertainty. The proposed method, namely the Stochastic Operator Network (SON), is constructed by combining the structure of the Deep Operator Network (DeepONet) with Stochastic Neural Networks (SNNs) to model stochasticity and enable probabilistic prediction. The training procedure is carried out by minimizing a Hamiltonian-type loss and optimizing the resulting objective using the Stochastic Maximum Principle. Numerical experiments on benchmark SPDEs under multiple uncertainty sources demonstrate the accuracy and robustness of the proposed method in capturing solution structure and quantifying predictive uncertainty.

Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by exploiting analytically tractable score functions, and have recently enabled supervised learning of efficient end-to-end generative samplers. Despite their empirical success, the training-free diffusion models lack rigorous and numerically verifiable error estimates. In this work, we develop a comprehensive error analysis for a class of training-free diffusion models used to generate labeled data for supervised learning of generative samplers. By exploiting the availability of the exact score function for Gaussian mixture models, our analysis avoids propagating score-function approximation errors through the reverse-time diffusion process and recovers classical convergence rates for ODE discretization schemes, such as first-order convergence for the Euler method. Moreover, the resulting error bounds exhibit favorable dimension dependence, scaling as O(d) in the ℓ_2 norm and O(log d) in the ℓ_∞ norm. Importantly, the proposed error estimates are fully numerically verifiable with respect to both time-step size and dimensionality, thereby bridging the gap between theoretical analysis and observed numerical behavior.

OBJECTIVE:To develop and validate a Vision Foundation Model-enhanced Multimodal Deep Learning Radiomics (VFM-MDLR) framework that integrates MR imaging with clinicopathological information for noninvasive prediction of deep myometrial invasion (DMI) in patients with endometrial cancer (EC). METHODS:This retrospective, multicenter study was conducted across seven independent centers and included 1376 EC patients. We developed a VFM-MDLR model based on two MRI sequences for the prediction of DMI. The framework was designed to first employ a General Knowledge Transfer across Heterogeneous-model (GKTH) subnetwork, which adaptively extracts general representations from vision foundation model (VFM). Building on this foundation, a Cross-Sequence Guided Attention (CSGA) module was incorporated to exploit the complementary information between CE-T1WI and T2WI, thereby achieving semantic alignment and synergistic feature representation. These features were then used to derive a deep-learning signature, termed VFM-enhanced Dual-sequence Knowledge Fusion (VFM-DKF), which was further integrated with key clinicopathological variables to construct the final VFM-MDLR predictor. Model performance was systematically evaluated in the internal validation cohort and four external cohorts, while interpretability was assessed using Grad-CAM and SHAP analyses. RESULTS:The VFM-MDLR model, which comprised age, histopathologic grade, the maximum tumor diameter (TMD), and the DLS, demonstrated the best predictive performance, with the highest AUC (0.832-0.877) across all cohorts. No significant difference was observed in performance for DMI detection between the VFM-MDLR model and experienced radiologists' readings (P = 0.915). CONCLUSION:The proposed VFM-MDLR model showed favorable accuracy in identifying DMI, potentially providing clinicians with a tool to facilitate individualized surgical treatment for patients with EC.

[This corrects the article DOI: 10.3389/fonc.2025.1666937.].

BACKGROUND:The prediction of Epidermal Growth Factor Receptor (EGFR) mutation status in advanced lung adenocarcinoma is crucial for targeted therapy. Since EGFR mutations manifest as both macroscopic imaging features on CT and microscopic morphological changes in tissue, integrating these multiscale signals is essential for a comprehensive diagnostic assessment. However, current related research faces two key limitations: on one hand, unimodal deep learning models suffer from limited representational power; on the other hand, existing multimodal methods fail to address the inherent data structural discrepancies between continuous CT and discrete WSI, often losing critical fine-grained details due to forced data compression or shared semantic bottlenecks. OBJECTIVE:To address the above limitations and improve the reliability of EGFR mutation status prediction, this study aims to propose a novel multimodal fusion framework (MFCA) that can effectively capture cross-modal semantic interactions and align imaging features across different scales. METHODS:A novel MFCA based on Cross-Attention (MFCA) is proposed, and its implementation steps are as follows: 1. First, a region-of-interest-guided approach is utilized to coarsely segment whole-slide histopathology images (WSI) into three constituent regions, namely cancerous, stromal, and other regions; 2. Then, a dual-branch encoder is employed to separately extract features from two types of imaging data-global features from Computed Tomography (CT) scans and region-specific features from the segmented WSI; 3. Critically, a bidirectional cross-attention module is introduced into the framework, which is designed to facilitate deep semantic interaction and alignment between the macroscopic context of CT imaging and the microscopic context of histopathology, thereby achieving highly efficient and discriminative feature fusion. RESULTS:On the external validation set, our MFCA framework achieved robust performance, with Area Under the Curve (AUC) values of 0.758(95% CI: 0.683-0.832) for cancerous regions, 0.805(95% CI: 0.716-0.900) for stromal regions, and 0.760(95% CI: 0.686-0.833) for other regions. The model's performance, particularly in the stromal component, was statistically superior to all baseline and competing models. CONCLUSION:The proposed MFCA framework predicts EGFR mutation status by innovatively integrating macroscopic CT imaging with region-specific microscopic WSI features. It serves as a valuable computational tool to support precision oncology for patients with advanced lung adenocarcinoma.

Large-language-model (LLM) agents for wireless systems have emerged rapidly, but nearly all of them live at the text or network-management layer. Knowledge-layer models answer questions about signals, orchestration-layer agents route intents over text and KPI metadata, and image-layer prompting operates on pre-computed CSI heatmaps; none of these consume or produce raw physical-layer RF signals. We introduce SenseAgent, a signal-grounded wireless sensing agent organized as a training-free mixture of experts (MoE-TF-DM), in which each expert is a training-free diffusion module specialized for one RF modality (RFID activity, WiFi CSI, or IQ modulation) and an LLM serves as both the modality gate and the natural-language interpreter over 11 signal-processing tools. Unlike classical mixture-of-experts baselines for wireless, whose priors live in pretrained expert weights and require retraining for each new class or environment, SenseAgent’s experts bind the prior to reference samples and adapt at inference time from a handful of few-shot exemplars. We support this architecture with a tool-selection evaluation harness of 30 natural-language queries that exercises top-1 accuracy, description robustness, and an LLM-only ablation. The agent reaches 96.7% top-1 tool selection at verbose default, drops to 23.3% when tool descriptions are truncated to a single sentence, and falls to zero when the LLM is asked to produce the same outputs without any tools, confirming that the tool layer is constitutive rather than decorative. On RadioML 2016.10a, the training-free IQ expert improves over a source-only baseline on 28 of 30 benchmark cells spanning a range of few-shot budgets and signal-to-noise ratios, with a mean accuracy gain of 6.8 percentage points, while running at roughly 1/180-th the synthesis time of a matched trained DDPM, directly quantifying the advantage of a data-bound prior under few-shot target-domain conditions. Lightweight case studies across IQ modulation, RFID, and WiFi CSI exercise zero-retraining adaptation through the full ReAct loop. Full quantitative per-modality studies are the subject of ongoing journal-length work; this invited paper establishes the agent framework, its evaluation, and a research agenda for signal-grounded sensing agents in 6G AI-native networks.

. In this work, we study the stochastic optimal control (SOC) problem mainly from the probabilistic viewpoint, i.e., via the stochastic maximum principle (SMP) [30]. We adopt the sample-wise backpropagation scheme proposed in [1] to solve the SOC problem under the strong convexity assumption. Importantly, in the stochastic gradient descent (SGD) procedure, we use batch samples with a higher-order scheme in the forward SDE to improve the convergence rate in [1] from O(root N/K + 1/N) to similar to O(root 1/K + 1/N-2), and note that the main source of uncertainty originates from the scheme for the simulation of the Z term in the BSDE. In the meantime, we note the SGD procedure uses only the necessary condition of the SMP, while the batch simulation of the approximating solution of BSDEs allows one to obtain a more accurate estimate of the control u that minimizes the Hamiltonian. We then propose a damped contraction algorithm to solve the SOC problem, and a proof of convergence for a special case is attained under appropriate assumptions. We then show numerical results to check the first-order convergence rate of the projection algorithm and analyze the convergence behavior of the damped contraction algorithm. We note that comparisons between the numerical results from these two algorithms (projection and contraction) show the projection approach is still favored in terms of stability and efficiency. Lastly, we briefly discuss how to incorporate the proposed scheme in solving practical problems, especially when randomized neural networks are used. We note that in this special case, the backward propagation error can be avoided, and parameter updates can be achieved via purely algebraic computation (vector algebra), which will potentially improve the efficiency of the whole training procedure. Such ideas will require further exploration, and we will leave this as our future work.

In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remains challenging because of the curse of dimensionality, which severely limits the scalability of classical numerical methods. Our approach builds on the recently developed finite expression method (FEX), which approximates PDE solutions in a function space generated by finitely many analytic expressions. This framework has been shown to achieve high, and in some cases machine-level, accuracy with polynomial memory complexity and favorable computational cost. We propose an extension of FEX in which the functional pool is generated by shallow neural network operators whose parameters are initialized using the transferable neural network method TransNet. Numerical experiments suggest that the proposed extension is an effective alternative for solving several high-dimensional PDEs.

Data assimilation blends model forecasts with observations to estimate the evolving state of complex dynamical systems, but sparse observing networks remain challenging because unobserved state variables are not directly constrained by observations. In this work, we introduce the Ensemble Score Filter with Linear Regression (EnSF-LR), a two-step filtering method for partially observed nonlinear systems. At each analysis time, EnSF-LR first applies the Ensemble Score Filter (EnSF) to update the observed state components using a nonlinear score-based analysis update. It then computes the resulting observed-state analysis increments and maps these corrections to the unobserved components through the ensemble-based prior covariance matrix. The latter amounts to the same linear regression mechanism used by Ensemble Kalman Filters (EnKFs). We evaluate EnSF-LR using the Lorenz-63 and 40-dimensional Lorenz-96 systems with sparse linear and nonlinear observations. The method is compared with the original EnSF and with the classical stochastic EnKF. In the linear-observation experiments, EnSF-LR produces accuracy comparable to the EnKF baseline while substantially reducing error relative to the original EnSF. In the nonlinear-observation experiments, EnSF-LR achieves lower full-state root-mean-square error than both the original EnSF and the EnKF reference. These results suggest that hybridizing score-based and EnKF analysis schemes provides an effective strategy for assimilating sparse and nonlinear observations.

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods depends on the observation network characteristics. In this study, we present initial experiments with the surface quasi-geostrophic model, in which we compare a recently developed ensemble filter using score-based diffusion models with the standard Local Ensemble Transform Kalman Filter (LETKF). Our results show that the analysis solutions respond differently to the number, spatial distribution, and nonlinear fraction of assimilated observations. We also find notable changes in the multiscale characteristics of the analysis errors. Given that standard DA techniques will eventually be replaced by more advanced methods, we hope this study sets the ground for future efforts to reassess the value of Earth observing systems in the context of newly emerging algorithms.

Background To develop a multicenter clinical-deep learning fusion (CDLF) model based on a robust federated multi-model collaboration (RFMC) framework for preoperative differentiation of solitary granulomatous nodules (SGN) from solid lung adenocarcinoma (SLAC) in patients with solitary pulmonary solid nodules (SPSNs). Methods We retrospectively enrolled 999 patients with surgically resected, histologically confirmed SPSNs from five centers, including 684 SLACs and 315 SGNs. The RFMC framework, incorporating robust knowledge transfer and sample distillation, was used to learn center-specific features and derive Personalized Federated Learning Signatures (PFLS). PFLS were combined with key clinical variables, including age, sex, mean nodule size, lobulation, spiculation, and nodule location, to build the CDLF model. Diagnostic performance was evaluated using area under the receiver operating characteristic curve (AUC), decision curve analysis (DCA), integrated discrimination improvement (IDI), and net reclassification improvement (NRI). Results PFLS showed robust discrimination across the five center-specific test sets, with AUCs of 0.807–0.886 (mean, 0.850). After integration with clinical indicators, CDLF further improved discrimination in all centers, achieving AUCs of 0.875–0.933 (mean, 0.897), with absolute AUC gains of 0.023–0.068 over PFLS. Compared with the clinical model and other federated learning models, CDLF provided significantly better risk stratification, with positive IDI and NRI across centers (all p < 0.05). DCA confirmed greater net clinical benefit for CDLF across relevant threshold probabilities. Conclusion CDLF enables reliable preoperative differentiation of SGN from SLAC in patients with SPSNs across multiple centers and may assist clinical decision-making.

Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management. In practice, however, complete and timely measurements may not always be available, and the observed data can be partial, noisy, or delayed. This motivates the use of learned forecasting models for predicting the evolving consumption state, together with data assimilation methods for sequential forecast correction. In this work, we study a high-dimensional data assimilation problem for real energy-consumption data. The forward prediction is supplied by a pretrained black-box spatio-temporal forecasting model, which is treated as the state propagator in the filtering procedure. We employ the Ensemble Score Filter (EnSF) to assimilate partial and noisy observations and to correct the forecast trajectory over time. The EnSF uses score-based diffusion models to approximate filtering distributions and avoids retraining neural-network score models during assimilation by using a closed-form score representation and Monte Carlo approximation. Numerical experiments demonstrate that open-loop propagation of the learned forecasting model can become unreliable over long horizons, while EnSF-based correction substantially improves state estimation. Comparisons with the Ensemble Kalman Filter (EnKF) further show that EnSF provides stronger correction under the nonlinear observation setting considered in this work.

This paper tackles the intricate task of jointly estimating state and parameters in data assimilation for stochastic dynamical systems that are affected by noise and observed only partially. While the concept of "optimal filtering" serves as the customary approach to estimate the state of the target dynamical system, traditional methods such as Kalman filters and particle filters encounter significant challenges when dealing with high-dimensional and nonlinear problems. When we also consider the scenario where the model parameters are unknown, the problem transforms into a joint state-parameter estimation problem. Presently, the leading-edge technique known as the Augmented Ensemble Kalman Filter (AugEnKF) addresses this issue by treating unknown parameters as additional state variables and employing the Ensemble Kalman Filter to estimate the augmented state-parameter vector. Despite its considerable progress, AugEnKF does exhibit certain limitations in terms of accuracy and stability. To address these challenges, we introduce an innovative approach, referred to as the United Filter. This method combines a remarkably stable and efficient ensemble score filter (EnSF) for state estimation with a precise direct filter dedicated to online parameter estimation. Utilizing the EnSF's generative capabilities grounded in diffusion models, the United Filter iteratively fine-tunes both state and parameter estimates within a single temporal data assimilation step. Thanks to the robustness of the EnSF, the proposed United Filter method offers a promising solution for enhancing our understanding and modeling of dynamical systems, as demonstrated by results from numerical experiments.

In this paper, we investigate the numerical approximation of optimal control problems for a class of stochastic partial differential equations (SPDEs) under partial observation. The system dynamics evolve in an infinite-dimensional Hilbert space and are driven by a cylindrical Wiener process, while observations are available in a finite-dimensional Euclidean space. We first derive a stochastic maximum principle (SMP) characterizing necessary conditions for optimality, with the associated adjoint processes formulated as backward SPDEs. We propose a numerical scheme based on the stochastic maximum principle that iteratively updates the control using stochastic gradient descent, combined with a particle filtering algorithm to estimate the conditional distribution of the system state. Numerical experiments illustrate the effectiveness of the proposed method.

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

Numerical modeling and simulation of two-phase flow in porous media is challenging due to the uncertainties in key parameters, such as permeability. To address these challenges, we propose a computational framework by utilizing the novel Ensemble Score Filter (EnSF) to enhance the accuracy of state estimation for two-phase flow systems in porous media. The forward simulation of the two-phase flow model is implemented using a mixed finite element method, which ensures accurate approximation of the pressure, the velocity, and the saturation. The EnSF leverages score-based diffusion models to approximate filtering distributions efficiently, avoiding the computational expense of neural network-based methods. By incorporating a closed-form score approximation and an analytical update mechanism, the EnSF overcomes degeneracy issues and handles high-dimensional nonlinear filtering with minimal computational overhead. Numerical experiments demonstrate the capabilities of EnSF in scenarios with uncertain permeability and incomplete observational data.

Accurate weather and climate prediction relies on data assimilation (DA), which estimates the Earth system state by integrating observations with models. While exascale computing has significantly advanced earth simulation, scalable and accurate inference of the Earth system state remains a fundamental bottleneck, limiting uncertainty quantification and prediction of extreme events. We introduce a unified one-stage generative DA framework that reformulates assimilation as Bayesian posterior sampling, replacing the conventional forecast-update cycle with compute-dense, GPU-efficient inference. At the core is STORM, a novel spatiotemporal transformer with a global attention linear-complexity scaling algorithm that breaks the quadratic attention barrier. On 32,768 GPUs of the Frontier supercomputer, our method achieves 63

Purpose To develop and validate a deep learning model integrating tumor and visceral adipose tissue (VAT) CT scan features with clinical indicators to predict postoperative peritoneal metastasis in serosa-invasive gastric cancer. Materials and Methods This multicenter, retrospective study between April 2008 and January 2018 included patients with pathologically confirmed serosa-invasive gastric cancer. Patients were divided into training, internal test, and independent external test sets. Tumor and VAT regions were segmented at preoperative CT. Deep features were extracted using a ResNet18 network. A fused tumor-VAT deep learning signature (F-DLS) was generated, incorporating clinical variables into a multimodal deep learning radiomics model (MDLR) using a sparse Bayesian extreme learning machine. Model performance was assessed using receiver operating characteristic curve, integrated discrimination improvement, calibration, decision curve analysis, and recurrence-free survival. Results Among 416 patients (mean age, 56.6 years ± 11.6; 66.1% male patients), the F-DLS achieved area under the receiver operating characteristic curve (AUC) values of 0.81 (95% CI: 0.73, 0.88) in the internal test set and 0.79 (95% CI: 0.71, 0.86) in the external test set. Compared with the tumor tissue DLS and VAT-DLS, the F-DLS showed numerically higher AUCs without statistical significance. The MDLR achieved the strongest predictive performance, with AUCs of 0.86 (95% CI: 0.79, 0.92) in the internal test set and 0.86 (95% CI: 0.78, 0.92) in the external test set. The MDLR statistically significantly outperformed clinical and deep learning-only models (integrated discrimination improvement, P < .001), showed good calibration, and provided favorable net benefit on decision curve analysis. High-risk patients identified by the MDLR had significantly shorter recurrence-free survival (log-rank P < .001). Conclusion The MDLR integrating CT scan features and clinical indicators enabled noninvasive prediction of peritoneal metastasis risk in serosa-invasive gastric cancer and may facilitate postoperative risk stratification. Keywords: Gastric Cancer, Peritoneal Metastasis, CT, Visceral Adipose Tissue, Deep Learning Supplemental material is available for this article. © RSNA, 2026.