Control of plasma turbulence remains a long-standing challenge in magnetically confined fusion research. Here, we explore a reinforcement-learning (RL) approach for bidirectional control of the turbulence-zonal-flow transition in the modified Hasegawa-Wakatani system, a minimal model of electrostatic drift-wave turbulence. Within our model, a weak zonal drag damps the otherwise long-lived zonal structures, giving them a finite lifetime and restoring the drive-damping balance required for repeatable transitions within finite control episodes; meanwhile, actuation is applied through a spatially distributed Gaussian source field under a time-weighted budget constraint on actuation costs. The plasma model is then coupled to CNN-based soft actor-critic and twin-delayed deterministic policy-gradient agents through a GPU-native JAX solver that is highly optimized for fast online training. In the turbulence-suppression task, the learned budget-aware schedule achieves the lowest time-integrated turbulent flux for a given consumed budget, outperforming both constant and linearly decreasing baselines across all tested unseen initial conditions. In the inverse zonal-break task, the agent discovers an up-down antisymmetric actuation pattern that induces radial E× B convection, disrupts the zonal structure, and sustains the turbulent state. A physics-informed warm-buffer initialization facilitates this discovery, as random exploration alone struggles to locate the narrow optimal manifold within the vast action space. These results demonstrate reinforcement learning as a practical trajectory optimizer for nonlinear plasma dynamics, such as turbulence control, and highlight the importance of physics guidance in such applications.

Complex microstructural pattern formation, such as dendrite growth, occurs across a wide range of materials and plays a crucial role in determining their properties and functional performance. While the phase-field method is a powerful computational approach for modeling microstructure dynamics, its substantial computational cost limits its integration into practical materials design workflows. Here, we introduce a machine-learning framework that employs autoregressive deep surrogates, trained on short trajectories from quantitative phase-field simulations of alloy solidification within limited spatial domains. Once trained, these surrogates accurately predict dendritic evolution over extended length and time scales, achieving speed-ups exceeding two orders of magnitude. We demonstrate the effectiveness of this approach through examples of isothermal growth and directional solidification of a dilute Al–Cu alloy, confirming its capability to predict complex microstructural pattern formation. Quantitative comparisons with phase-field benchmarks reveal excellent agreement in the tip-selection constant, morphological symmetry, and primary spacing evolution, further validating our approach.

The non-equilibrium dynamics of mesoscale phase transitions are fundamentally shaped by thermal fluctuations, which not only seed instabilities but actively control kinetic pathways, including rare barrier-crossing events such as nucleation that are entirely inaccessible to deterministic models. Machine-learning surrogates for such systems must therefore represent stochasticity explicitly, enforce conservation laws by construction, and expose physically interpretable structure. We develop physics-aware surrogate models for the stochastic Cahn-Hilliard equation in 3D that satisfy all three requirements simultaneously. The key innovation is to parameterize the surrogate at the level of inter-cell fluxes, decomposing each flux into a deterministic mobility-weighted chemical-potential gradient and a learnable noise amplitude. This design guarantees exact mass conservation at every step and adds physical fluctuations to inter-cell mass transport. A learnable free energy functional provides thermodynamic interpretability, validated by independent recovery of the bulk double-well landscape, interfacial excess energy, and curvature-independent interfacial tension. Tests demonstrate accurate reproduction of ensemble statistics and noise-accelerated coarsening, with generalization to spatial domains 64 times larger in volume and temporal horizons 160x longer than those seen during training. Critically, the stochastic surrogate captures thermally activated nucleation in the metastable regime, a qualitative capability that no deterministic surrogate can provide regardless of training, thus establishing flux-level stochasticity as an architectural necessity rather than an optional enhancement.

Active flow control is a fundamental application in engineering. Recent advances in deep reinforcement learning have made progress in this field. However, the classical online RL approaches require extensive real-time interactions with the high fidelity environment, while each sensor configuration change necessitates whole policy retraining. All these factors result in prohibitive computational costs for real-world applications. In this work, we propose a novel offline RL framework that addresses both challenges through data-driven policy extraction. We develop a sensor position-conditioned architecture that enables a single policy network to adapt seamlessly to multiple sensor arrangements. The position-conditioned approach incorporated spatial relationship modeling through Point Attention layers to ensure the generalizability to varying sensor placements. We demonstrate the framework on two representative problems, mitigating chaoticity in the Kuramoto-Sivashinsky equation and flow control over airfoils governed by the Navier-Stokes equation. The result demonstrates that the policy extraction from the dataset provides unprecedented flexibility for sensor placement optimization. This approach represents a significant step towards adaptive, intelligent flow control systems.

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.

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.

Extracting the explicit governing equations of a dynamic system from limited data has attracted increasing attention in the data-driven modeling community. Compared to black-box learning approaches, the sparse-regression-based learning method enables discovering an analytical model form from data, which is more appealing due to its white-box nature. However, distilling explicit equations from real-world measurements with data uncertainty is challenging, where many existing methods are less robust. Moreover, it is unclear how to efficiently learn a parametric system from multiple data sets with different parameters. This paper presents a group sparse Bayesian learning approaches to uncover the explicit model forms of a parametric dynamical system with estimated uncertainties. A deep neural network is constructed to improve the calculation of derivatives from noisy measurements. Group sparsity is leveraged to enable synchronous learning from a group of parametric datasets governed by the equations with the same functional form but different parameter settings. The proposed approach has been studied over a few linear/nonlinear ODE systems in explicit and implicit settings. In particular, a simplified parametric model of intracranial dynamics was identified from multiple synthetic datasets with different patient-specific parameters. The numerical results demonstrated the effectiveness of the proposed approach and the merit of synchronous learning from multiple datasets in a group sparsifying Bayesian setting.

Accurate prediction of dynamical systems in unstructured meshes has recently shown successes in scientific simulations. Many dynamical systems have a nonnegligible level of stochasticity introduced by various factors (e.g. chaoticity), so there is a need for a unified framework that captures both deterministic and stochastic components in the rollouts of these systems. Inspired by regeneration learning, we propose a new model that combines generative and sequential networks to model dynamical systems. Specifically, we use an autoencoder to learn compact representations of full-space physical variables in a low-dimensional space. We then integrate a transformer with a conditional normalizing flow model to model the temporal sequence of latent representations. We evaluate the new model in both deterministic and stochastic systems. The model outperforms several competitive baseline models and makes more accurate predictions of deterministic systems. Its own prediction error is also reflected in its uncertainty estimations. When predicting stochastic systems, the proposed model generates high-quality rollout samples. The mean and variance of these samples well match the statistics of samples computed from expensive numerical simulations.

In this research paper, we study the capability of artificial neural network models to emulate storm surge based on the storm track/size/intensity history, leveraging a database of synthetic storm simulations. Traditionally, computational fluid dynamics (CFD) solvers are employed to numerically solve the storm surge governing equations that correspond to expensive to evaluate partial differential equations (PDE). This study presents a neural network model that can predict storm surge, informed by a database of synthetic storm simulations. This model can serve as a fast and affordable emulator for the expensive CFD solvers creating the original database. The neural network model is trained with the storm track parameters used to drive the CFD solvers, and the output of the model is the time-series evolution of the predicted storm surge across multiple nodes within the spatial domain of interest. Once the model is trained, it can be deployed for further predictions based on new storm track inputs. The developed neural network model is a time-series model, composed of a long short-term memory (LSTM), a variation of recurrent neural network (RNN), further enriched with convolutional neural networks (CNNs). The convolutional neural network is employed to capture the correlation of data spatially (across the aforementioned nodes). Therefore, the temporal and spatial correlations of data are captured by the combination of the mentioned models, representing the ConvLSTM model. As the problem is a sequence to sequence time-series problem, an encoder–decoder ConvLSTM model is designed. Furthermore, the performance of the developed convolutional recurrent neural network model is improved by residual connection networks. Additional techniques are employed in the process of model training to enrich the model performance that the model can learn from the data in a more effective way. The performance of the developed model is compared with the results provided by a Gaussian process (GP) implementation, representing a state-of-the-art alternative for establishing time-series emulation of storm surge predictions. The results show that the proposed convolutional recurrent neural network outperforms the GP implementation for the examined synthetic storm database.

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.

This paper proposes a deep learning-based generalized empirical flow model (EFM) that can provide a fast and accurate prediction of the glottal flow during normal phonation. The approach is based on the assumption that the vibration of the vocal folds can be represented by a universal kinematics equation (UKE), which is used to generate a glottal shape library. For each shape in the library, the ground truth values of the flow rate and pressure distribution are obtained from the high-fidelity Navier-Stokes (N-S) solution. A fully connected deep neural network (DNN) is then trained to build the empirical mapping between the shapes and the flow rate and pressure distributions. The obtained DNN-based EFM is coupled with a finite element method (FEM)-based solid dynamics solver for fluid-structure-interaction (FSI) simulation of phonation. The EFM is evaluated by comparing the N-S solutions in both static glottal shapes and FSI simulations. The results demonstrate a good prediction performance in accuracy and efficiency.

Finding amorphous polymers with higher thermal conductivity is important, as they are ubiquitous in heat transfer applications. With recent progress in material informatics, machine learning approaches have been increasingly adopted for finding or designing materials with desired properties. However, relatively limited effort has been put into finding thermally conductive polymers using machine learning, mainly due to the lack of polymer thermal conductivity databases with reasonable data volume. In this work, we combine high-throughput molecular dynamics (MD) simulations and machine learning to explore polymers with relatively high thermal conductivity (> 0.300 W/m-K). We first randomly select 365 polymers from the existing PolyInfo database and calculate their thermal conductivity using MD simulations. The data are then employed to train a machine learning regression model to quantify the structure-thermal conductivity relation, which is further leveraged to screen polymer candidates in the PolyInfo database with thermal conductivity > 0.300 W/m-K. 133 polymers with MD-calculated thermal conductivity above this threshold are eventually identified. Polymers with a wide range of thermal conductivity values are selected for re-calculation under different simulation conditions, and those polymers found with thermal conductivity above 0.300 W/m-K are mostly calculated to maintain values above this threshold despite fluctuation in the exact values. A classification model is also constructed, and similar results were obtained compared to the regression model in predicting polymers with thermal conductivity above or below 0.300 W/m-K. The strategy and results from this work may contribute to automating the design of polymers with high thermal conductivity.

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all different classes of deep neural networks, the convolutional neural network (CNN) has attracted increasing attention in the scientific machine learning community, since the parameter-sharing feature in CNN enables efficient learning for problems with large-scale spatiotemporal fields. However, one of the biggest challenges is that CNN only can handle regular geometries with image-like format (i.e., rectangular domains with uniform grids). In this paper, we propose a novel physics-constrained CNN learning architecture, aiming to learn solutions of parametric PDEs on irregular domains without any labeled data. In order to leverage powerful classic CNN backbones, elliptic coordinate mapping is introduced to enable coordinate transforms between the irregular physical domain and regular reference domain. The proposed method has been assessed by solving a number of PDEs on irregular domains, including heat equations and steady Navier-Stokes equations with parameterized boundary conditions and varying geometries. Moreover, the proposed method has also been compared against the state-of-the-art PINN with fully-connected neural network (FC-NN) formulation. The numerical results demonstrate the effectiveness of the proposed approach and exhibit notable superiority over the FC-NN based PINN in terms of efficiency and accuracy.

High-resolution (HR) information of fluid flows, although preferable, is usually less accessible due to limited computational or experimental resources. In many cases, fluid data are generally sparse, incomplete, and possibly noisy. How to enhance spatial resolution and decrease the noise level of flow data is essential and practically useful. Deep learning (DL) techniques have been demonstrated to be effective for super-resolution (SR) tasks, which, however, primarily rely on sufficient HR labels for training. In this work, we present a novel physics-informed DL-based SR solution using convolutional neural networks (CNNs), which is able to produce HR flow fields from low-resolution (LR) inputs in high-dimensional parameter space. By leveraging the conservation laws and boundary conditions of fluid flows, the CNN-SR model is trained without any HR labels. Moreover, the proposed CNN-SR solution unifies the forward SR and inverse data assimilation for the scenarios where the physics is partially known, e.g., unknown boundary conditions. A new network structure is designed to enable not only the parametric SR but also the parametric inference for the first time. Several flow SR problems relevant to cardiovascular applications have been studied to demonstrate the proposed method's effectiveness and merit. A series of different LR scenarios, including LR input with Gaussian noises, non-Gaussian magnetic resonance imaging noises, and downsampled measurements given either well-posed or ill-posed physics, are investigated to illustrate the SR, denoising, and inference capabilities of the proposed method.

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers. Due to complicated nature of the physics and geometry, such process can be computational prohibitive for most real-time applications and many-query analyses. Therefore, developing a cost-effective surrogate model is of great practical significance. Deep learning (DL) has shown new promises for surrogate modeling due to its capability of handling strong nonlinearity and high dimensionality. However, the off-the-shelf DL architectures fail to operate when the data becomes sparse. Unfortunately, data is often insufficient in most parametric fluid dynamics problems since each data point in the parameter space requires an expensive numerical simulation based on the first principle, e.g., Naiver--Stokes equations. In this paper, we provide a physics-constrained DL approach for surrogate modeling of fluid flows without relying on any simulation data. Specifically, a structured deep neural network (DNN) architecture is devised to enforce the initial and boundary conditions, and the governing partial differential equations are incorporated into the loss of the DNN to drive the training. Numerical experiments are conducted on a number of internal flows relevant to hemodynamics applications, and the forward propagation of uncertainties in fluid properties and domain geometry is studied as well. The results show excellent agreement on the flow field and forward-propagated uncertainties between the DL surrogate approximations and the first-principle numerical simulations.

In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physics-constrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.