Jian-Xun Wang

Han Gao, Xu Han, Jiaoyang Huang et al.

Recently the Transformer structure has shown good performances in graph learning tasks. However, these Transformer models directly work on graph nodes and may have difficulties learning high-level information. Inspired by the vision transformer, which applies to image patches, we propose a new Transformer-based graph neural network: Patch Graph Transformer (PatchGT). Unlike previous transformer-based models for learning graph representations, PatchGT learns from non-trainable graph patches, not from nodes directly. It can help save computation and improve the model performance. The key idea is to segment a graph into patches based on spectral clustering without any trainable parameters, with which the model can first use GNN layers to learn patch-level representations and then use Transformer to obtain graph-level representations. The architecture leverages the spectral information of graphs and combines the strengths of GNNs and Transformers. Further, we show the limitations of previous hierarchical trainable clusters theoretically and empirically. We also prove the proposed non-trainable spectral clustering method is permutation invariant and can help address the information bottlenecks in the graph. PatchGT achieves higher expressiveness than 1-WL-type GNNs, and the empirical study shows that PatchGT achieves competitive performances on benchmark datasets and provides interpretability to its predictions. The implementation of our algorithm is released at our Github repo: https://github.com/tufts-ml/PatchGT.

Xin-Yang Liu, Min Zhu, Lu Lu et al.

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by ``baking'' the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers', and Navier-Stokes equations.

Fangzheng Sun, Yang Liu, Jian-Xun Wang et al.

Nonlinear dynamics is ubiquitous in nature and commonly seen in various science and engineering disciplines. Distilling analytical expressions that govern nonlinear dynamics from limited data remains vital but challenging. To tackle this fundamental issue, we propose a novel Symbolic Physics Learner (SPL) machine to discover the mathematical structure of nonlinear dynamics. The key concept is to interpret mathematical operations and system state variables by computational rules and symbols, establish symbolic reasoning of mathematical formulas via expression trees, and employ a Monte Carlo tree search (MCTS) agent to explore optimal expression trees based on measurement data. The MCTS agent obtains an optimistic selection policy through the traversal of expression trees, featuring the one that maps to the arithmetic expression of underlying physics. Salient features of the proposed framework include search flexibility and enforcement of parsimony for discovered equations. The efficacy and superiority of the SPL machine are demonstrated by numerical examples, compared with state-of-the-art baselines.

Pan Du, Xiaozhi Zhu, Jian-Xun Wang

Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant challenges, particularly when it comes to complex 3D patient-specific shapes in the real world. First, it is notoriously challenging to parameterize the input space of arbitrarily complex 3-D geometries. Second, the process often involves massive forward simulations, which are extremely computationally demanding or even infeasible. We propose a novel deep learning surrogate modeling solution to address these challenges and enable rapid hemodynamic predictions. Specifically, a statistical generative model for 3-D patient-specific shapes is developed based on a small set of baseline patient-specific geometries. An unsupervised shape correspondence solution is used to enable geometric morphing and scalable shape synthesis statistically. Moreover, a simulation routine is developed for automatic data generation by automatic meshing, boundary setting, simulation, and post-processing. An efficient supervised learning solution is proposed to map the geometric inputs to the hemodynamics predictions in latent spaces. Numerical studies on aortic flows are conducted to demonstrate the effectiveness and merit of the proposed techniques.

Luning Sun, Daniel Zhengyu Huang, Hao Sun et al.

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us understand and predict the behavior of complex dynamic systems. Although extensive work has recently been done in this field, robustly distilling explicit model forms from very sparse data with considerable noise remains intractable. Moreover, quantifying and propagating the uncertainty of the identified system from noisy data is challenging, and relevant literature is still limited. To bridge this gap, we develop a novel Bayesian spline learning framework to identify parsimonious governing equations of nonlinear (spatio)temporal dynamics from sparse, noisy data with quantified uncertainty. The proposed method utilizes spline basis to handle the data scarcity and measurement noise, upon which a group of derivatives can be accurately computed to form a library of candidate model terms. The equation residuals are used to inform the spline learning in a Bayesian manner, where approximate Bayesian uncertainty calibration techniques are employed to approximate posterior distributions of the trainable parameters. To promote the sparsity, an iterative sequential-threshold Bayesian learning approach is developed, using the alternative direction optimization strategy to systematically approximate L0 sparsity constraints. The proposed algorithm is evaluated on multiple nonlinear dynamical systems governed by canonical ordinary and partial differential equations, and the merit/superiority of the proposed method is demonstrated by comparison with state-of-the-art methods.

Pu Ren, Chengping Rao, Su Chen et al.

There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these geophysical problems are typically defined in large domains (i.e., semi-infinite), which leads to high computational cost. In this paper, we present a novel physics-informed neural network (PINN) model for seismic wave modeling in semi-infinite domain without the nedd of labeled data. In specific, the absorbing boundary condition is introduced into the network as a soft regularizer for handling truncated boundaries. In terms of computational efficiency, we consider a sequential training strategy via temporal domain decomposition to improve the scalability of the network and solution accuracy. Moreover, we design a novel surrogate modeling strategy for parametric loading, which estimates the wave propagation in semin-infinite domain given the seismic loading at different locations. Various numerical experiments have been implemented to evaluate the performance of the proposed PINN model in the context of forward modeling of seismic wave propagation. In particular, we define diverse material distributions to test the versatility of this approach. The results demonstrate excellent solution accuracy under distinctive scenarios.

Han Gao, Xu Han, Xiantao Fan et al.

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. We introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, and scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: 1) the synthesis of LES simulated instantaneous flow sequences from URANS inputs; 2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; 3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation.

Pu Ren, Chengping Rao, Yang Liu et al.

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on the coarse-grained simulations, which is of cheap computational expense and retains satisfactory solution accuracy. However, the major existing work focuses on data-driven approaches which rely on rich training datasets and lack sufficient physical constraints. To this end, we propose a novel and efficient spatiotemporal super-resolution framework via physics-informed learning, inspired by the independence between temporal and spatial derivatives in partial differential equations (PDEs). The general principle is to leverage the temporal interpolation for flow estimation, and then introduce convolutional-recurrent neural networks for learning temporal refinement. Furthermore, we employ the stacked residual blocks with wide activation and sub-pixel layers with pixelshuffle for spatial reconstruction, where feature extraction is conducted in a low-resolution latent space. Moreover, we consider hard imposition of boundary conditions in the network to improve reconstruction accuracy. Results demonstrate the superior effectiveness and efficiency of the proposed method compared with baseline algorithms through extensive numerical experiments.

Deepak Akhare, Zeping Chen, Richard Gulotty et al.

Chemical vapor infiltration (CVI) is a widely adopted manufacturing technique used in producing carbon-carbon and carbon-silicon carbide composites. These materials are especially valued in the aerospace and automotive industries for their robust strength and lightweight characteristics. The densification process during CVI critically influences the final performance, quality, and consistency of these composite materials. Experimentally optimizing the CVI processes is challenging due to long experimental time and large optimization space. To address these challenges, this work takes a modeling-centric approach. Due to the complexities and limited experimental data of the isothermal CVI densification process, we have developed a data-driven predictive model using the physics-integrated neural differentiable (PiNDiff) modeling framework. An uncertainty quantification feature has been embedded within the PiNDiff method, bolstering the model's reliability and robustness. Through comprehensive numerical experiments involving both synthetic and real-world manufacturing data, the proposed method showcases its capability in modeling densification during the CVI process. This research highlights the potential of the PiNDiff framework as an instrumental tool for advancing our understanding, simulation, and optimization of the CVI manufacturing process, particularly when faced with sparse data and an incomplete description of the underlying physics.

Delin An, Pan Du, Pengfei Gu et al.

Accurate segmentation of the aorta and its associated arch branches is crucial for diagnosing aortic diseases. While deep learning techniques have significantly improved aorta segmentation, they remain challenging due to the intricate multiscale structure and the complexity of the surrounding tissues. This paper presents a novel approach for enhancing aorta segmentation using a Bayesian neural network-based hierarchical Laplacian of Gaussian (LoG) model. Our model consists of a 3D U-Net stream and a hierarchical LoG stream: the former provides an initial aorta segmentation, and the latter enhances blood vessel detection across varying scales by learning suitable LoG kernels, enabling self-adaptive handling of different parts of the aorta vessels with significant scale differences. We employ a Bayesian method to parameterize the LoG stream and provide confidence intervals for the segmentation results, ensuring robustness and reliability of the prediction for vascular medical image analysts. Experimental results show that our model can accurately segment main and supra-aortic vessels, yielding at least a 3% gain in the Dice coefficient over state-of-the-art methods across multiple volumes drawn from two aorta datasets, and can provide reliable confidence intervals for different parts of the aorta. The code is available at https://github.com/adlsn/LoGBNet.

Meet Hemant Parikh, Yaqin Chen, Jian-Xun Wang

Data assimilation and scientific inverse problems require reconstructing high-dimensional physical states from sparse and noisy observations, ideally with uncertainty-aware posterior samples that remain faithful to learned priors and governing physics. While training-free conditional generation is well developed for diffusion models, corresponding conditioning and posterior sampling strategies for Flow Matching (FM) priors remain comparatively under-explored, especially on scientific benchmarks where fidelity must be assessed beyond measurement misfit. In this work, we study training-free conditional generation for scientific inverse problems under FM priors and organize existing inference-time strategies by where measurement information is injected: (i) guided transport dynamics that perturb sampling trajectories using likelihood information, and (ii) source-distribution inference that performs posterior inference over the source variable while keeping the learned transport fixed. Building on the latter, we propose D-Flow SGLD, a source-space posterior sampling method that augments differentiable source inference with preconditioned stochastic gradient Langevin dynamics, enabling scalable exploration of the source posterior induced by new measurement operators without retraining the prior or modifying the learned FM dynamics. We benchmark representative methods from both families on a hierarchy of problems: 2D toy posteriors, chaotic Kuramoto-Sivashinsky trajectories, and wall-bounded turbulence reconstruction. Across these settings, we quantify trade-offs among measurement assimilation, posterior diversity, and physics/statistics fidelity, and establish D-Flow SGLD as a practical FM-compatible posterior sampler for scientific inverse problems.

Pan Du, Yongqi Li, Mingqi Xu et al.

Differentiable programming has emerged as a structural prerequisite for gradient-based inverse problems and end-to-end hybrid physics--machine learning in computational fluid dynamics. However, existing differentiable CFD platforms are confined to structured Cartesian grids, excluding the geometrically complex domains where body-conforming unstructured discretizations are indispensable. We present DiFVM, the first GPU-accelerated, end-to-end differentiable finite-volume CFD solver operating natively on unstructured polyhedral meshes. The key enabling insight is a structural isomorphism between finite-volume discretization and graph neural network message-passing: by reformulating all FVM operators as static scatter/gather primitives on the mesh connectivity graph, DiFVM transforms irregular unstructured connectivity into a first-class GPU data structure. All operations are implemented in JAX/XLA, providing just-in-time compilation, operator fusion, and automatic differentiation through the complete simulation pipeline. Differentiable Windkessel outlet boundary conditions are provided for cardiovascular applications, and DiFVM accepts standard OpenFOAM case directories without modification for seamless adoption in existing workflows. Forward validation across benchmarks spanning canonical flows to patient-specific hemodynamics demonstrates close agreement with OpenFOAM, and end-to-end differentiability is demonstrated through inference of Windkessel parameters from sparse observations. DiFVM bridges the critical gap between differentiable programming and unstructured-mesh CFD, enabling gradient-based inverse problems and physics-integrated machine learning on complex engineering geometries.

Qi Wang, Pu Ren, Hao Zhou et al.

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently, machine learning has been increasingly utilized to solve PDE problems, but they often encounter challenges related to interpretability, generalizability, and strong dependency on rich labeled data. Hence, we introduce a new PDE-Preserved Coarse Correction Network (P$^2$C$^2$Net) to efficiently solve spatiotemporal PDE problems on coarse mesh grids in small data regimes. The model consists of two synergistic modules: (1) a trainable PDE block that learns to update the coarse solution (i.e., the system state), based on a high-order numerical scheme with boundary condition encoding, and (2) a neural network block that consistently corrects the solution on the fly. In particular, we propose a learnable symmetric Conv filter, with weights shared over the entire model, to accurately estimate the spatial derivatives of PDE based on the neural-corrected system state. The resulting physics-encoded model is capable of handling limited training data (e.g., 3--5 trajectories) and accelerates the prediction of PDE solutions on coarse spatiotemporal grids while maintaining a high accuracy. P$^2$C$^2$Net achieves consistent state-of-the-art performance with over 50\% gain (e.g., in terms of relative prediction error) across four datasets covering complex reaction-diffusion processes and turbulent flows.

Deepak Akhare, Tengfei Luo, Jian-Xun Wang

The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive capabilities and show great potential for data-driven modeling of complex physical systems. However, a critical and yet unaddressed challenge lies in the quantification of inherent uncertainties stemming from multiple sources. Addressing this gap, we introduce a novel method, DiffHybrid-UQ, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models, leveraging the strengths of deep ensemble Bayesian learning and nonlinear transformations. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity. This is achieved within a Bayesian model averaging framework, where aleatoric uncertainties are modeled through hybrid neural models. The unscented transformation plays a pivotal role in enabling the flow of these uncertainties through the nonlinear functions within the hybrid model. In contrast, epistemic uncertainties are estimated using an ensemble of stochastic gradient descent (SGD) trajectories. This approach offers a practical approximation to the posterior distribution of both the network parameters and the physical parameters. Notably, the DiffHybrid-UQ framework is designed for simplicity in implementation and high scalability, making it suitable for parallel computing environments. The merits of the proposed method have been demonstrated through problems governed by both ordinary and partial differentiable equations.

Xin-Yang Liu, Meet Hemant Parikh, Xiantao Fan et al.

Eddy-resolving turbulence simulations require stochastic inflow conditions that accurately replicate the complex, multi-scale structures of turbulence. Traditional recycling-based methods rely on computationally expensive precursor simulations, while existing synthetic inflow generators often fail to reproduce realistic coherent structures of turbulence. Recent advances in deep learning (DL) have opened new possibilities for inflow turbulence generation, yet many DL-based methods rely on deterministic, autoregressive frameworks prone to error accumulation, resulting in poor robustness for long-term predictions. In this work, we present CoNFiLD-inlet, a novel DL-based inflow turbulence generator that integrates diffusion models with a conditional neural field (CNF)-encoded latent space to produce realistic, stochastic inflow turbulence. By parameterizing inflow conditions using Reynolds numbers, CoNFiLD-inlet generalizes effectively across a wide range of Reynolds numbers ($Re_τ$ between $10^3$ and $10^4$) without requiring retraining or parameter tuning. Comprehensive validation through a priori and a posteriori tests in Direct Numerical Simulation (DNS) and Wall-Modeled Large Eddy Simulation (WMLES) demonstrates its high fidelity, robustness, and scalability, positioning it as an efficient and versatile solution for inflow turbulence synthesis.

Deepak Akhare, Pan Du, Tengfei Luo et al.

Hybrid neural-physics modeling frameworks through differentiable programming have emerged as powerful tools in scientific machine learning, enabling the integration of known physics with data-driven learning to improve prediction accuracy and generalizability. However, most existing hybrid frameworks rely on explicit recurrent formulations, which suffer from numerical instability and error accumulation during long-horizon forecasting. In this work, we introduce Im-PiNDiff, a novel implicit physics-integrated neural differentiable solver for stable and accurate modeling of spatiotemporal dynamics. Inspired by deep equilibrium models, Im-PiNDiff advances the state using implicit fixed-point layers, enabling robust long-term simulation while remaining fully end-to-end differentiable. To enable scalable training, we introduce a hybrid gradient propagation strategy that integrates adjoint-state methods with reverse-mode automatic differentiation. This approach eliminates the need to store intermediate solver states and decouples memory complexity from the number of solver iterations, significantly reducing training overhead. We further incorporate checkpointing techniques to manage memory in long-horizon rollouts. Numerical experiments on various spatiotemporal PDE systems, including advection-diffusion processes, Burgers' dynamics, and multi-physics chemical vapor infiltration processes, demonstrate that Im-PiNDiff achieves superior predictive performance, enhanced numerical stability, and substantial reductions in memory and runtime cost relative to explicit and naive implicit baselines. This work provides a principled, efficient, and scalable framework for hybrid neural-physics modeling.

Pan Du, Delin An, Chaoli Wang et al.

Image-based modeling is essential for understanding cardiovascular hemodynamics and advancing the diagnosis and treatment of cardiovascular diseases. Constructing patient-specific vascular models remains labor-intensive, error-prone, and time-consuming, limiting their clinical applications. This study introduces a deep-learning framework that automates the creation of simulation-ready vascular models from medical images. The framework integrates a segmentation module for accurate voxel-based vessel delineation with a surface deformation module that performs anatomically consistent and unsupervised surface refinements guided by medical image data. By unifying voxel segmentation and surface deformation into a single cohesive pipeline, the framework addresses key limitations of existing methods, enhancing geometric accuracy and computational efficiency. Evaluated on publicly available datasets, the proposed approach demonstrates state-of-the-art performance in segmentation and mesh quality while significantly reducing manual effort and processing time. This work advances the scalability and reliability of image-based computational modeling, facilitating broader applications in clinical and research settings.

Pan Du, Mingqi Xu, Xiaozhi Zhu et al.

Accurate characterization of vascular geometry is essential for cardiovascular diagnosis and treatment planning. Traditional statistical shape modeling (SSM) methods rely on linear assumptions, limiting their expressivity and scalability to complex topologies such as multi-branch vascular structures. We introduce HUG-VAS, a Hierarchical NURBS Generative model for Vascular geometry Synthesis, which integrates NURBS surface parameterization with diffusion-based generative modeling to synthesize realistic, fine-grained aortic geometries. Trained with 21 patient-specific samples, HUG-VAS generates anatomically faithful aortas with supra-aortic branches, yielding biomarker distributions that closely match those of the original dataset. HUG-VAS adopts a hierarchical architecture comprising a denoising diffusion model that generates centerlines and a guided diffusion model that synthesizes radial profiles conditioned on those centerlines, thereby capturing two layers of anatomical variability. Critically, the framework supports zero-shot conditional generation from image-derived priors, enabling practical applications such as interactive semi-automatic segmentation, robust reconstruction under degraded imaging conditions, and implantable device optimization. To our knowledge, HUG-VAS is the first SSM framework to bridge image-derived priors with generative shape modeling via a unified integration of NURBS parameterization and hierarchical diffusion processes.

Luning Sun, Xin-Yang Liu, Siyan Zhao et al.

Controlling instabilities in complex dynamical systems is challenging in scientific and engineering applications. Deep reinforcement learning (DRL) has seen promising results for applications in different scientific applications. The many-query nature of control tasks requires multiple interactions with real environments of the underlying physics. However, it is usually sparse to collect from the experiments or expensive to simulate for complex dynamics. Alternatively, controlling surrogate modeling could mitigate the computational cost issue. However, a fast and accurate learning-based model by offline training makes it very hard to get accurate pointwise dynamics when the dynamics are chaotic. To bridge this gap, the current work proposes a multi-fidelity reinforcement learning (MFRL) framework that leverages differentiable hybrid models for control tasks, where a physics-based hybrid model is corrected by limited high-fidelity data. We also proposed a spectrum-based reward function for RL learning. The effect of the proposed framework is demonstrated on two complex dynamics in physics. The statistics of the MFRL control result match that computed from many-query evaluations of the high-fidelity environments and outperform other SOTA baselines.

Junyi Guo, Pan Du, Xiantao Fan et al.

We investigate conditional neural fields (CNFs), mesh-agnostic, coordinate-based decoders conditioned on a low-dimensional latent, for spatial dimensionality reduction of turbulent flows. CNFs are benchmarked against Proper Orthogonal Decomposition and a convolutional autoencoder within a unified encoding-decoding framework and a common evaluation protocol that explicitly separates in-range (interpolative) from out-of-range (strict extrapolative) testing beyond the training horizon, with identical preprocessing, metrics, and fixed splits across all baselines. We examine three conditioning mechanisms: (i) activation-only modulation (often termed FiLM), (ii) low-rank weight and bias modulation (termed FP), and (iii) last-layer inner-product coupling, and introduce a novel domain-decomposed CNF that localizes complexities. Across representative turbulence datasets (WMLES channel inflow, DNS channel inflow, and wall pressure fluctuations over turbulent boundary layers), CNF-FP achieves the lowest training and in-range testing errors, while CNF-FiLM generalizes best for out-of-range scenarios once moderate latent capacity is available. Domain decomposition significantly improves out-of-range accuracy, especially for the more demanding datasets. The study provides a rigorous, physics-aware basis for selecting conditioning, capacity, and domain decomposition when using CNFs for turbulence compression and reconstruction.

Zhao Feng, Xin-Yang Liu, Meet Hemant Parikh et al.

Geological Carbon Sequestration (GCS) has emerged as a promising strategy for mitigating global warming, yet its effectiveness heavily depends on accurately characterizing subsurface flow dynamics. The inherent geological uncertainty, stemming from limited observations and reservoir heterogeneity, poses significant challenges to predictive modeling. Existing methods for inverse modeling and uncertainty quantification are computationally intensive and lack generalizability, restricting their practical utility. Here, we introduce a Conditional Neural Field Latent Diffusion (CoNFiLD-geo) model, a generative framework for efficient and uncertainty-aware forward and inverse modeling of GCS processes. CoNFiLD-geo synergistically combines conditional neural field encoding with Bayesian conditional latent-space diffusion models, enabling zero-shot conditional generation of geomodels and reservoir responses across complex geometries and grid structures. The model is pretrained unconditionally in a self-supervised manner, followed by a Bayesian posterior sampling process, allowing for data assimilation for unseen/unobserved states without task-specific retraining. Comprehensive validation across synthetic and real-world GCS scenarios demonstrates CoNFiLD-geo's superior efficiency, generalization, scalability, and robustness. By enabling effective data assimilation, uncertainty quantification, and reliable forward modeling, CoNFiLD-geo significantly advances intelligent decision-making in geo-energy systems, supporting the transition toward a sustainable, net-zero carbon future.

Delin An, Pan Du, Jian-Xun Wang et al.

Accurate 3D aortic construction is crucial for clinical diagnosis, preoperative planning, and computational fluid dynamics (CFD) simulations, as it enables the estimation of critical hemodynamic parameters such as blood flow velocity, pressure distribution, and wall shear stress. Existing construction methods often rely on large annotated training datasets and extensive manual intervention. While the resulting meshes can serve for visualization purposes, they struggle to produce geometrically consistent, well-constructed surfaces suitable for downstream CFD analysis. To address these challenges, we introduce AortaDiff, a diffusion-based framework that generates smooth aortic surfaces directly from CT/MRI volumes. AortaDiff first employs a volume-guided conditional diffusion model (CDM) to iteratively generate aortic centerlines conditioned on volumetric medical images. Each centerline point is then automatically used as a prompt to extract the corresponding vessel contour, ensuring accurate boundary delineation. Finally, the extracted contours are fitted into a smooth 3D surface, yielding a continuous, CFD-compatible mesh representation. AortaDiff offers distinct advantages over existing methods, including an end-to-end workflow, minimal dependency on large labeled datasets, and the ability to generate CFD-compatible aorta meshes with high geometric fidelity. Experimental results demonstrate that AortaDiff performs effectively even with limited training data, successfully constructing both normal and pathologically altered aorta meshes, including cases with aneurysms or coarctation. This capability enables the generation of high-quality visualizations and positions AortaDiff as a practical solution for cardiovascular research.

Zeping Chen, Marwa Yacouti, Maryam Shakiba et al.

Carbon fiber-reinforced composites (CFRC) are pivotal in advanced engineering applications due to their exceptional mechanical properties. A deep understanding of CFRC behavior under mechanical loading is essential for optimizing performance in demanding applications such as aerospace structures. While traditional Finite Element Method (FEM) simulations, including advanced techniques like Interface-enriched Generalized FEM (IGFEM), offer valuable insights, they can struggle with computational efficiency. Existing data-driven surrogate models partially address these challenges by predicting propagated damage or stress-strain behavior but fail to comprehensively capture the evolution of stress and damage throughout the entire deformation history, including crack initiation and propagation. This study proposes a novel auto-regressive composite U-Net deep learning model to simultaneously predict stress and damage fields during CFRC deformation. By leveraging the U-Net architecture's ability to capture spatial features and integrate macro- and micro-scale phenomena, the proposed model overcomes key limitations of prior approaches. The model achieves high accuracy in predicting evolution of stress and damage distribution within the microstructure of a CFRC under unidirectional strain, offering a speed-up of over 60 times compared to IGFEM.

Xin-Yang Liu, Dariush Bodaghi, Qian Xue et al.

Fish fin rays constitute a sophisticated control system for ray-finned fish, facilitating versatile locomotion within complex fluid environments. Despite extensive research on the kinematics and hydrodynamics of fish locomotion, the intricate control strategies in fin-ray actuation remain largely unexplored. While deep reinforcement learning (DRL) has demonstrated potential in managing complex nonlinear dynamics; its trial-and-error nature limits its application to problems involving computationally demanding environmental interactions. This study introduces a cutting-edge off-policy DRL algorithm, interacting with a fluid-structure interaction (FSI) environment to acquire intricate fin-ray control strategies tailored for various propulsive performance objectives. To enhance training efficiency and enable scalable parallelism, an innovative asynchronous parallel training (APT) strategy is proposed, which fully decouples FSI environment interactions and policy/value network optimization. The results demonstrated the success of the proposed method in discovering optimal complex policies for fin-ray actuation control, resulting in a superior propulsive performance compared to the optimal sinusoidal actuation function identified through a parametric grid search. The merit and effectiveness of the APT approach are also showcased through comprehensive comparison with conventional DRL training strategies in numerical experiments of controlling nonlinear dynamics.

Xu Han, Han Gao, Tobias Pfaff et al.

Graph-based next-step prediction models have recently been very successful in modeling complex high-dimensional physical systems on irregular meshes. However, due to their short temporal attention span, these models suffer from error accumulation and drift. In this paper, we propose a new method that captures long-term dependencies through a transformer-style temporal attention model. We introduce an encoder-decoder structure to summarize features and create a compact mesh representation of the system state, to allow the temporal model to operate on a low-dimensional mesh representations in a memory efficient manner. Our method outperforms a competitive GNN baseline on several complex fluid dynamics prediction tasks, from sonic shocks to vascular flow. We demonstrate stable rollouts without the need for training noise and show perfectly phase-stable predictions even for very long sequences. More broadly, we believe our approach paves the way to bringing the benefits of attention-based sequence models to solving high-dimensional complex physics tasks.

Xin-Yang Liu, Jian-Xun Wang

Model-based reinforcement learning (MBRL) is believed to have much higher sample efficiency compared to model-free algorithms by learning a predictive model of the environment. However, the performance of MBRL highly relies on the quality of the learned model, which is usually built in a black-box manner and may have poor predictive accuracy outside of the data distribution. The deficiencies of the learned model may prevent the policy from being fully optimized. Although some uncertainty analysis-based remedies have been proposed to alleviate this issue, model bias still poses a great challenge for MBRL. In this work, we propose to leverage the prior knowledge of underlying physics of the environment, where the governing laws are (partially) known. In particular, we developed a physics-informed MBRL framework, where governing equations and physical constraints are utilized to inform the model learning and policy search. By incorporating the prior information of the environment, the quality of the learned model can be notably improved, while the required interactions with the environment are significantly reduced, leading to better sample efficiency and learning performance. The effectiveness and merit have been demonstrated over a handful of classic control problems, where the environments are governed by canonical ordinary/partial differential equations.

Jian-Xun Wang, Junji Huang, Lian Duan et al.

Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework has been demonstrated in several canonical incompressible flows. However, its performance on high-Mach-number flows is still not clear. In this work we use the PIML approach to predict the discrepancies in RANS modeled Reynolds stresses in high-Mach-number flat-plate turbulent boundary layers by using an existing DNS database. Specifically, the discrepancy function is first constructed using a DNS training flow and then used to correct RANS-predicted Reynolds stresses under flow conditions different from the DNS. The machine-learning technique is shown to significantly improve RANS-modeled turbulent normal stresses, the turbulent kinetic energy, and the Reynolds-stress anisotropy. Improvements are consistently observed when different training datasets are used. Moreover, a high-dimensional visualization technique and distance metrics are used to provide a priori assessment of prediction confidence based only on RANS simulations. This study demonstrates that the PIML approach is a computationally affordable technique for improving the accuracy of RANS-modeled Reynolds stresses for high-Mach-number turbulent flows when there is a lack of experiments and high-fidelity simulations.