- Date: April 12, 2024
MERL Contact: Saviz Mowlavi
Research Areas: Control, Dynamical Systems, Machine Learning, Optimization
Brief - Saviz Mowlavi was invited to present remotely at the Computational and Applied Mathematics seminar series in the Department of Mathematics at North Carolina State University.
The talk, entitled "Model-based and data-driven prediction and control of spatio-temporal systems", described the use of temporal smoothness to regularize the training of fast surrogate models for PDEs, user-friendly methods for PDE-constrained optimization, and efficient strategies for learning feedback controllers for PDEs.
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- Date & Time: Wednesday, March 1, 2023; 1:00 PM
Speaker: Shaowu Pan, Rensselaer Polytechnic Institute
MERL Host: Saviz Mowlavi
Research Areas: Computational Sensing, Data Analytics, Machine Learning
Abstract 
High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace. Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to make solutions computationally tractable in real-time. Common existing paradigms for dimensionality reduction include linear methods, such as the singular value decomposition (SVD), and nonlinear methods, such as variants of convolutional autoencoders (CAE). However, these encoding techniques lack the ability to efficiently represent the complexity associated with spatio-temporal data, which often requires variable geometry, non-uniform grid resolution, adaptive meshing, and/or parametric dependencies. To resolve these practical engineering challenges, we propose a general framework called Neural Implicit Flow (NIF) that enables a mesh-agnostic, low-rank representation of large-scale, parametric, spatial-temporal data. NIF consists of two modified multilayer perceptrons (MLPs): (i) ShapeNet, which isolates and represents the spatial complexity, and (ii) ParameterNet, which accounts for any other input complexity, including parametric dependencies, time, and sensor measurements. We demonstrate the utility of NIF for parametric surrogate modeling, enabling the interpretable representation and compression of complex spatio-temporal dynamics, efficient many-spatial-query tasks, and improved generalization performance for sparse reconstruction.
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- Date: December 2, 2022 - December 8, 2022
MERL Contacts: Matthew Brand; Toshiaki Koike-Akino; Jing Liu; Saviz Mowlavi; Kieran Parsons; Ye Wang
Research Areas: Artificial Intelligence, Control, Dynamical Systems, Machine Learning, Signal Processing
Brief - In addition to 5 papers in recent news (https://www.merl.com/news/news-20221129-1450), MERL researchers presented 2 papers at the NeurIPS Conference Workshop, which was held Dec. 2-8. NeurIPS is one of the most prestigious and competitive international conferences in machine learning.
- “Optimal control of PDEs using physics-informed neural networks” by Saviz Mowlavi and Saleh Nabi
Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a neural network-based surrogate model for the unknown state, PINNs can seamlessly blend measurement data with physical constraints. Here, we extend this framework to PDE-constrained optimal control problems, for which the governing PDE is fully known and the goal is to find a control variable that minimizes a desired cost objective. We validate the performance of the PINN framework by comparing it to state-of-the-art adjoint-based optimization, which performs gradient descent on the discretized control variable while satisfying the discretized PDE.
- “Learning with noisy labels using low-dimensional model trajectory” by Vasu Singla, Shuchin Aeron, Toshiaki Koike-Akino, Matthew E. Brand, Kieran Parsons, Ye Wang
Noisy annotations in real-world datasets pose a challenge for training deep neural networks (DNNs), detrimentally impacting generalization performance as incorrect labels may be memorized. In this work, we probe the observations that early stopping and low-dimensional subspace learning can help address this issue. First, we show that a prior method is sensitive to the early stopping hyper-parameter. Second, we investigate the effectiveness of PCA, for approximating the optimization trajectory under noisy label information. We propose to estimate the low-rank subspace through robust and structured variants of PCA, namely Robust PCA, and Sparse PCA. We find that the subspace estimated through these variants can be less sensitive to early stopping, and can outperform PCA to achieve better test error when trained on noisy labels.
- In addition, new MERL researcher, Jing Liu, also presented a paper entitled “CoPur: Certifiably Robust Collaborative Inference via Feature Purification" based on his previous work before joining MERL. His paper was elected as a spotlight paper to be highlighted in lightening talks and featured paper panel.
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