Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Ampere equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems.
相關內容
For turbulent problems of industrial scale, computational cost may become prohibitive due to the stability constraints associated with explicit time discretization of the underlying conservation laws. On the other hand, implicit methods allow for larger time-step sizes but require exorbitant computational resources. Implicit-explicit (IMEX) formulations combine both temporal approaches, using an explicit method in nonstiff portions of the domain and implicit in stiff portions. While these methods can be shown to be orders of magnitude faster than typical explicit discretizations, they are still limited by their implicit discretization in terms of cost. Hybridization reduces the scaling of these systems to an effective lower dimension, which allows the system to be solved at significant speedup factors compared to standard implicit methods. This work proposes an IMEX scheme that combines hybridized and standard flux reconstriction (FR) methods to tackle geometry-induced stiffness. By using the so-called transmission conditions, an overall conservative formulation can be obtained after combining both explicit FR and hybridized implicit FR methods. We verify and apply our approach to a series of numerical examples, including a multi-element airfoil at Reynolds number 1.7 million. Results demonstrate speedup factors of four against standard IMEX formulations and at least 15 against standard explicit formulations for the same problem.
This work addresses the development of a physics-informed neural network (PINN) with a loss term derived from a discretized time-dependent reduced-order system. In this work, first, the governing equations are discretized using a finite difference scheme (whereas, any other discretization technique can be adopted), then projected on a reduced or latent space using the Proper Orthogonal Decomposition (POD)-Galerkin approach and next, the residual arising from discretized reduced order equation is considered as an additional loss penalty term alongside the data-driven loss term using different variants of deep learning method such as Artificial neural network (ANN), Long Short-Term Memory based neural network (LSTM). The LSTM neural network has been proven to be very effective for time-dependent problems in a purely data-driven environment. The current work demonstrates the LSTM network's potential over ANN networks in physics-informed neural networks (PINN) as well. The potential of using discretized governing equations instead of continuous form lies in the flexibility of input to the PINN. Different sizes of data ranging from small, medium to big datasets are used to assess the potential of discretized-physics-informed neural networks when there is very sparse or no data available. The proposed methods are applied to a pitch-plunge airfoil motion governed by rigid-body dynamics and a one-dimensional viscous Burgers' equation. The current work also demonstrates the prediction capability of various discretized-physics-informed neural networks outside the domain where the data is available or governing equation-based residuals are minimized.
Numerical models have long been used to understand geoscientific phenomena, including tidal currents, crucial for renewable energy production and coastal engineering. However, their computational cost hinders generating data of varying resolutions. As an alternative, deep learning-based downscaling methods have gained traction due to their faster inference speeds. But most of them are limited to only inference fixed scale and overlook important characteristics of target geoscientific data. In this paper, we propose a novel downscaling framework for tidal current data, addressing its unique characteristics, which are dissimilar to images: heterogeneity and local dependency. Moreover, our framework can generate any arbitrary-scale output utilizing a continuous representation model. Our proposed framework demonstrates significantly improved flow velocity predictions by 93.21% (MSE) and 63.85% (MAE) compared to the Baseline model while achieving a remarkable 33.2% reduction in FLOPs.
Many scientific and technological problems are related to optimization. Among them, black-box optimization in high-dimensional space is particularly challenging. Recent neural network-based black-box optimization studies have shown noteworthy achievements. However, their capability in high-dimensional search space is still limited. This study proposes a black-box optimization method based on the evolution strategy (ES) and the generative neural network (GNN) model. We designed the algorithm so that the ES and the GNN model work cooperatively. This hybrid model enables reliable training of surrogate networks; it optimizes multi-objective, high-dimensional, and stochastic black-box functions. Our method outperforms baseline optimization methods in this experiment, including ES, and Bayesian optimization.
Virtual garment simulation has become increasingly important with applications in garment design and virtual try-on. However, reproducing garments faithfully remains a cumbersome process. We propose an end-to-end method for estimating parameters of shell material models corresponding to real fabrics with minimal priors. Our method determines yarn model properties from information directly obtained from real fabrics, unlike methods that require expensive specialized capture systems. We use an extended homogenization method to match yarn-level and shell-level hyperelastic energies with respect to a range of surface deformations represented by the first and second fundamental forms, including bending along the diagonal to warp and weft directions. We optimize the parameters of a shell deformation model involving uncoupled bending and membrane energies. This allows the simulated model to exhibit nonlinearity and anisotropy seen in real cloth. Finally, we validate our results with quantitative and visual comparisons against real world fabrics through stretch tests and drape experiments. Our homogenized shell models not only capture the characteristics of underlying yarn patterns, but also exhibit distinct behaviors for different yarn materials.
Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can result in substantially different outputs of a neural network. Safety-critical environments require neural networks that are robust against input perturbations. However, training and formally verifying robust neural networks is challenging. We address this challenge by employing, for the first time, a end-to-end set-based training procedure that trains robust neural networks for formal verification. Our training procedure drastically simplifies the subsequent formal robustness verification of the trained neural network. While previous research has predominantly focused on augmenting neural network training with adversarial attacks, our approach leverages set-based computing to train neural networks with entire sets of perturbed inputs. Moreover, we demonstrate that our set-based training procedure effectively trains robust neural networks, which are easier to verify. In many cases, set-based trained neural networks outperform neural networks trained with state-of-the-art adversarial attacks.
IPv6 is a fundamentally different Internet Protocol than IPv4, and IPv6-only networks cannot, by default, communicate with the IPv4 Internet. This lack of interoperability necessitates complex mechanisms for incremental deployment and bridging networks so that non-dual-stack systems can interact with the whole Internet. NAT64 is one such bridging mechanism by which a network allows IPv6-only clients to connect to the entire Internet, leveraging DNS to identify IPv4-only networks, inject IPv6 response addresses pointing to an internal gateway, and seamlessly translate connections. To date, our understanding of NAT64 deployments is limited; what little information exists is largely qualitative, taken from mailing lists and informal discussions. In this work, we present a first look at the active measurement of NAT64 deployment on the Internet focused on deployment prevalence, configuration, and security. We seek to measure NAT64 via two distinct large-scale measurements: 1) open resolvers on the Internet, and 2) client measurements from RIPE Atlas. For both datasets, we broadly find that despite substantial anecdotal reports of NAT64 deployment, measurable deployments are exceedingly sparse. While our measurements do not preclude the large-scale deployment of NAT64, they do point to substantial challenges in measuring deployments with our existing best-known methods. Finally, we also identify problems in NAT64 deployments, with gateways not following the RFC specification and also posing potential security risks.
Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.
Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191