Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPhysics-informed Tensor-train ConvLSTM for Volumetric Velocity Forecasting
110
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
According to the National Academies, a weekly forecast of velocity, vertical structure, and duration of the Loop Current (LC) and its eddies is critical for understanding the oceanography and ecosystem, and for mitigating outcomes of anthropogenic and natural disasters in the Gulf of Mexico (GoM). However, this forecast is a challenging problem since the LC behaviour is dominated by long-range spatial connections across multiple timescales. In this paper, we extend spatiotemporal predictive learning, showing its effectiveness beyond video prediction, to a 4D model, i.e., a novel Physics-informed Tensor-train ConvLSTM (PITT-ConvLSTM) for temporal sequences of 3D geospatial data forecasting. Specifically, we propose 1) a novel 4D higher-order recurrent neural network with empirical orthogonal function analysis to capture the hidden uncorrelated patterns of each hierarchy, 2) a convolutional tensor-train decomposition to capture higher-order space-time correlations, and 3) to incorporate prior physic knowledge that is provided from domain experts by informing the learning in latent space. The advantage of our proposed method is clear: constrained by physical laws, it simultaneously learns good representations for frame dependencies (both short-term and long-term high-level dependency) and inter-hierarchical relations within each time frame. Experiments on geospatial data collected from the GoM demonstrate that PITT-ConvLSTM outperforms the state-of-the-art methods in forecasting the volumetric velocity of the LC and its eddies for a period of over one week.
rate research
Read More
Locality preserving projections (LPP) are a classical dimensionality reduction method based on data graph information. However, LPP is still responsive to extreme outliers. LPP aiming for vectorial data may undermine data structural information when it is applied to multidimensional data. Besides, it assumes the dimension of data to be smaller than the number of instances, which is not suitable for high-dimensional data. For high-dimensional data analysis, the tensor-train decomposition is proved to be able to efficiently and effectively capture the spatial relations. Thus, we propose a tensor-train parameterization for ultra dimensionality reduction (TTPUDR) in which the traditional LPP mapping is tensorized in terms of tensor-trains and the LPP objective is replaced with the Frobenius norm to increase the robustness of the model. The manifold optimization technique is utilized to solve the new model. The performance of TTPUDR is assessed on classification problems and TTPUDR significantly outperforms the past methods and the several state-of-the-art methods.
Recurrent Neural Networks (RNNs) represent the de facto standard machine learning tool for sequence modelling, owing to their expressive power and memory. However, when dealing with large dimensional data, the corresponding exponential increase in the number of parameters imposes a computational bottleneck. The necessity to equip RNNs with the ability to deal with the curse of dimensionality, such as through the parameter compression ability inherent to tensors, has led to the development of the Tensor-Train RNN (TT-RNN). Despite achieving promising results in many applications, the full potential of the TT-RNN is yet to be explored in the context of interpretable financial modelling, a notoriously challenging task characterized by multi-modal data with low signal-to-noise ratio. To address this issue, we investigate the potential of TT-RNN in the task of financial forecasting of currencies. We show, through the analysis of TT-factors, that the physical meaning underlying tensor decomposition, enables the TT-RNN model to aid the interpretability of results, thus mitigating the notorious black-box issue associated with neural networks. Furthermore, simulation results highlight the regularization power of TT decomposition, demonstrating the superior performance of TT-RNN over its uncompressed RNN counterpart and other tensor forecasting methods.
Most methods for dimensionality reduction are based on either tensor representation or local geometry learning. However, the tensor-based methods severely rely on the assumption of global and multilinear structures in high-dimensional data; and the manifold learning methods suffer from the out-of-sample problem. In this paper, bridging the tensor decomposition and manifold learning, we propose a novel method, called Hypergraph Regularized Nonnegative Tensor Factorization (HyperNTF). HyperNTF can preserve nonnegativity in tensor factorization, and uncover the higher-order relationship among the nearest neighborhoods. Clustering analysis with HyperNTF has low computation and storage costs. The experiments on four synthetic data show a desirable property of hypergraph in uncovering the high-order correlation to unfold the curved manifolds. Moreover, the numerical experiments on six real datasets suggest that HyperNTF robustly outperforms state-of-the-art algorithms in clustering analysis.
Reduced models describing the Lagrangian dynamics of the Velocity Gradient Tensor (VGT) in Homogeneous Isotropic Turbulence (HIT) are developed under the Physics-Informed Machine Learning (PIML) framework. We consider VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and sub-filter contributions, which is accomplished by constructing them using the integrity bases and invariants of VGT. The developed models can be expressed using the extended Tensor Basis Neural Network (TBNN). Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number Direct Numerical Simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the ground-truth DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into TBNN.
While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the knowledge is given less explicitly. In this work, we propose a novel architecture called Differentiable Physics-informed Graph Networks (DPGN) to incorporate implicit physics knowledge which is given from domain experts by informing it in latent space. Using the concept of DPGN, we demonstrate that climate prediction tasks are significantly improved. Besides the experiment results, we validate the effectiveness of the proposed module and provide further applications of DPGN, such as inductive learning and multistep predictions.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
