•Enable CNN-based physics-informed deep learning for PDEs on irregular domain.•The proposed network can be trained without any labeled data.•Boundary conditions are strictly encoded in a hard ...manner.•Investigated complex parametric PDEs, e.g., Naiver-Stokes with varying geometries.•Shows improvements of efficiency and accuracy over FC-NN formulations.
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 steady-state PDEs on irregular domains, including heat equations, Navier-Stokes equations, and Poisson equations with parameterized boundary conditions, varying geometries, and spatially-varying source fields. 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.
Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation using polynomials into a finite-dimensional algebraic system. ...Due to the multi-scale nature of the physics and sensitivity from meshing a complicated geometry, such process can be computational prohibitive for most real-time applications (e.g., clinical diagnosis and surgery planning) and many-query analyses (e.g., optimization design and uncertainty quantification). 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, success of which heavily relies on the large amount of training data and interpolatory nature of the problem, 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., Navier–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 (i.e., Navier–Stokes 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.
•Proposed a simulation-free, physics-constrained deep learning for surrogate CFD model.•Boundary-encoded neural network outperforms the one with soft boundary constraints.•Demonstrated effectiveness of the label-free learning on a few vascular flows.
Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential ...of physics-informed neural networks (PINNs) to solve PDEs as a basis for data-driven modeling and inverse analysis. However, the majority of existing PINN methods, based on fully-connected NNs, pose intrinsic limitations to low-dimensional spatiotemporal parameterizations. Moreover, since the initial/boundary conditions (I/BCs) are softly imposed via penalty, the solution quality heavily relies on hyperparameter tuning. To this end, we propose the novel physics-informed convolutional-recurrent learning architectures (PhyCRNet and PhyCRNet-s) for solving PDEs without any labeled data. Specifically, an encoder–decoder convolutional long short-term memory network is proposed for low-dimensional spatial feature extraction and temporal evolution learning. The loss function is defined as the aggregated discretized PDE residuals, while the I/BCs are hard-encoded in the network to ensure forcible satisfaction (e.g., periodic boundary padding). The networks are further enhanced by autoregressive and residual connections that explicitly simulate time marching. The performance of our proposed methods has been assessed by solving three nonlinear PDEs (e.g., 2D Burgers’ equations, the λ-ω and FitzHugh Nagumo reaction–diffusion equations), and compared against the start-of-the-art baseline algorithms. The numerical results demonstrate the superiority of our proposed methodology in the context of solution accuracy, extrapolability and generalizability.
•Presented a novel physics-informed discrete learning strategy for solving PDEs without any labeled data.•Proposed an encoder–decoder convolutional-recurrent scheme for low-dimensional feature learning.•Employed hard-encoding of initial and boundary conditions.•Incorporated autoregressive and residual connections to explicitly simulate time marching.•Demonstrated excellent solution accuracy, extrapolability and generalizability of the proposed methodology.
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.
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and ...realistic applications. First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement. Second, the infinite search space over-complicates the non-convex optimization for network training. Third, although the convolutional neural network (CNN)-based discrete learning can significantly improve training efficiency, CNNs struggle to handle irregular geometries with unstructured meshes. To properly address these challenges, we present a novel discrete PINN framework based on graph convolutional network (GCN) and variational structure of PDE to solve forward and inverse partial differential equations (PDEs) in a unified manner. The use of a piecewise polynomial basis can reduce the dimension of search space and facilitate training and convergence. Without the need of tuning penalty parameters in classic PINNs, the proposed method can strictly impose boundary conditions and assimilate sparse data in both forward and inverse settings. The flexibility of GCNs is leveraged for irregular geometries with unstructured meshes. The effectiveness and merit of the proposed method are demonstrated over a variety of forward and inverse computational mechanics problems governed by both linear and nonlinear PDEs.
Necrosis is one of the main forms of cardiomyocyte death in heart disease. Recent studies have demonstrated that certain types of necrosis are regulated and programmed dependent on the activation of ...receptor-interacting serine/threonine-protein kinase (RIPK) 1 and 3 which may be negatively regulated by Fas-associated protein with death domain (FADD). In addition, microRNAs and long noncoding RNAs have been shown to play important roles in various biological processes recently.
The purpose of this study was to test the hypothesis that microRNA-103/107 and H19 can participate in the regulation of RIPK1- and RIPK3-dependent necrosis in fetal cardiomyocyte-derived H9c2 cells and myocardial infarction through targeting FADD.
Our results show that FADD participates in H2O2-induced necrosis by influencing the formation of RIPK1 and RIPK3 complexes in H9c2 cells. We further demonstrate that miR-103/107 target FADD directly. Knockdown of miR-103/107 antagonizes necrosis in the cellular model and also myocardial infarction in a mouse ischemia/reperfusion model. The miR-103/107-FADD pathway does not participate in tumor necrosis factor-α-induced necrosis. In exploring the molecular mechanism by which miR-103/107 are regulated, we show that long noncoding RNA H19 directly binds to miR-103/107 and regulates FADD expression and necrosis.
Our results reveal a novel myocardial necrosis regulation model, which is composed of H19, miR-103/107, and FADD. Modulation of their levels may provide a new approach for preventing myocardial necrosis.
Sustained cardiac hypertrophy accompanied by maladaptive cardiac remodelling represents an early event in the clinical course leading to heart failure. Maladaptive hypertrophy is considered to be a ...therapeutic target for heart failure. However, the molecular mechanisms that regulate cardiac hypertrophy are largely unknown.
Here we show that a circular RNA (circRNA), which we term heart-related circRNA (HRCR), acts as an endogenous miR-223 sponge to inhibit cardiac hypertrophy and heart failure. miR-223 transgenic mice developed cardiac hypertrophy and heart failure, whereas miR-223-deficient mice were protected from hypertrophic stimuli, indicating that miR-223 acts as a positive regulator of cardiac hypertrophy. We identified ARC as a miR-223 downstream target to mediate the function of miR-223 in cardiac hypertrophy. Apoptosis repressor with CARD domain transgenic mice showed reduced hypertrophic responses. Further, we found that a circRNA HRCR functions as an endogenous miR-223 sponge to sequester and inhibit miR-223 activity, which resulted in the increase of ARC expression. Heart-related circRNA directly bound to miR-223 in cytoplasm and enforced expression of HRCR in cardiomyocytes and in mice both exhibited attenuated hypertrophic responses.
These findings disclose a novel regulatory pathway that is composed of HRCR, miR-223, and ARC. Modulation of their levels provides an attractive therapeutic target for the treatment of cardiac hypertrophy and heart failure.
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