International Business Machines Corporation

Tufts University

Tel Aviv University

The Brigham and Women's Hospital, Inc.

Tel Aviv-yafo University

Misha E Kilmer

Lior Horesh

Haim Avron

Elizabeth Newman

David Nahamoo

Raya Horesh

Shashanka Ubaru

William Scott Hoge

Osman Asif Malik

Ning Hao

Jiani Zhang

Techniques for generating and managing, including simulating and training, deep tensor neural networks are presented. A deep tensor neural network comprises a graph of nodes connected via weighted edges. A network management component (NMC) extracts features from tensor-formatted input data based on tensor-formatted parameters. NMC evolves tensor-formatted input data based on a defined tensor-tensor layer evolution rule, the network generating output data based on evolution of the tensor-formatted input data. The network is activated by non-linear activation functions, wherein the weighted edges and non-linear activation functions operate, based on tensor-tensor functions, to evolve tensor-formatted input data. NMC trains the network based on tensor-formatted training data, comparing output training data output from the network to simulated output data, based on a defined loss function, to determine an update. NMC updates the network, including weight and bias parameters, based on the update, by application of tensor-tensor operations.

Generating and managing deep tensor neural networks

A computer-implemented method for analyzing a time-varying graph is provided. The time-varying graph includes nodes representing elements in a network, edges representing transactions between elements, and data associated with the nodes and the edges. The computer-implemented method includes constructing, using a processor, adjacency and feature matrices describing each node and edge of each time-varying graph for stacking into an adjacency tensor and describing the data of each time-varying graph for stacking into a feature tensor, respectively. The adjacency and feature tensors are partitioned into adjacency and feature training tensors and into adjacency and feature validation tensors, respectively. An embedding model and a prediction model are created using the adjacency and feature training tensors. The embedding and prediction models are validated using the adjacency and feature validation tensors to identify an optimized embedding-prediction model pair.

Tensor-based predictions from analysis of time-varying graphs

An illustrative embodiment includes a method for solving a dynamical system. The method comprises: obtaining multidimensional snapshots representing respective discrete solutions of the dynamical system; storing the multidimensional snapshots within a snapshot tensor having an order of at least three; generating a basis for at least a subspace of a state space of the dynamical system at least in part by performing a decomposition of the snapshot tensor; deriving a reduced order model at least in part by using the basis to project the dynamical system from the state space onto the subspace; and solving the reduced order model of the dynamical system.

Multi-linear dynamical model reduction

Methods and systems for generating output of a simulation model in a simulation system are described. In an example, a processor may retrieve observed output data from a memory. The observed output data may be generated based on a simulation operator of a simulation model. The processor may further optimize a generalization error of a distance measure between the observed output data and model output data. The model output data may be generated based on a high-fidelity operator. The processor may further determine a correction operator based on the optimized generalization error of the distance measure. The processor may further append the correction operator to the simulation operator to produce a supplemented operator. The processor may further generate supplemented output data by applying the simulation model with the supplemented operator on a set of inputs.

Mis-specified model supplementation

A tensor decomposition method, system, and computer program product include compressing multi-dimensional data by truncated tensor-tensor decompositions.

Optimal multi-dimensional data compression by tensor-tensor decompositions tensor

Reconstructing an image from MRI data provided by an MRI machine includes: selecting a system transformation based on the MRI machine; selecting a subspace based on the system transformation; and obtaining a solution vector that solves a minimization problem. The minimization problem is formulated on the subspace, based on the MRI data. The image is reconstructed from the solution vector and displayed.

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Medfield, MA, United States of America

Misha E Kilmer