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Learning Semilinear Neural Operators : A Unified Recursive Framework For Prediction And Data Assimilation
Feb 24, 2024
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead.
Inv-SENnet: Invariant Self Expression Network for clustering under biased data
Nov 13, 2022
Subspace clustering algorithms are used for understanding the cluster structure that explains the dataset well. These methods are extensively used for data-exploration tasks in various areas of Natural Sciences. However, most of these methods fail to handle unwanted biases in datasets. For datasets where a data sample represents multiple attributes, naively applying any clustering approach can result in undesired output. To this end, we propose a novel framework for jointly removing unwanted attributes (biases) while learning to cluster data points in individual subspaces. Assuming we have information about the bias, we regularize the clustering method by adversarially learning to minimize the mutual information between the data and the unwanted attributes. Our experimental result on synthetic and real-world datasets demonstrate the effectiveness of our approach.
Variation is the Norm: Brain State Dynamics Evoked By Emotional Video Clips
Oct 24, 2021
For the last several decades, emotion research has attempted to identify a "biomarker" or consistent pattern of brain activity to characterize a single category of emotion (e.g., fear) that will remain consistent across all instances of that category, regardless of individual and context. In this study, we investigated variation rather than consistency during emotional experiences while people watched video clips chosen to evoke instances of specific emotion categories. Specifically, we developed a sequential probabilistic approach to model the temporal dynamics in a participant's brain activity during video viewing. We characterized brain states during these clips as distinct state occupancy periods between state transitions in blood oxygen level dependent (BOLD) signal patterns. We found substantial variation in the state occupancy probability distributions across individuals watching the same video, supporting the hypothesis that when it comes to the brain correlates of emotional experience, variation may indeed be the norm.
A Distributed Model-Free Algorithm for Multi-hop Ride-sharing using Deep Reinforcement Learning
Oct 30, 2019
The growth of autonomous vehicles, ridesharing systems, and self driving technology will bring a shift in the way ride hailing platforms plan out their services. However, these advances in technology coupled with road congestion, environmental concerns, fuel usage, vehicles emissions, and the high cost of the vehicle usage have brought more attention to better utilize the use of vehicles and their capacities. In this paper, we propose a novel multi-hop ride-sharing (MHRS) algorithm that uses deep reinforcement learning to learn optimal vehicle dispatch and matching decisions by interacting with the external environment. By allowing customers to transfer between vehicles, i.e., ride with one vehicle for sometime and then transfer to another one, MHRS helps in attaining 30\% lower cost and 20\% more efficient utilization of fleets, as compared to the ride-sharing algorithms. This flexibility of multi-hop feature gives a seamless experience to customers and ride-sharing companies, and thus improves ride-sharing services.