- Date & Time: Tuesday, November 21, 2023; 11:00 AM
Speaker: Gioele Zardini, ETH Zürich and MIT
MERL Host: Karl Berntorp
Research Areas: Control, Dynamical Systems
Abstract 
When designing complex systems, we need to consider multiple trade-offs at various abstraction levels and scales, and choices of single components need to be studied jointly. For instance, the design of future mobility solutions (e.g., autonomous vehicles, micromobility) and the design of the mobility systems they enable are closely coupled. Indeed, knowledge about the intended service of novel mobility solutions would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management policies. Optimally co-designing sociotechnical systems is a complex task for at least two reasons. On one hand, the co-design of interconnected systems (e.g., large networks of cyber-physical systems) involves the simultaneous choice of components arising from heterogeneous natures (e.g., hardware vs. software parts) and fields, while satisfying systemic constraints and accounting for multiple objectives. On the other hand, components are connected via collaborative and conflicting interactions between different stakeholders (e.g., within an intermodal mobility system). In this talk, I will present a framework to co-design complex systems, leveraging a monotone theory of co-design and tools from game theory. The framework will be instantiated in the task of designing future mobility systems, all the way from the policies that a city can design, to the autonomy of vehicles part of an autonomous mobility-on-demand service. Through various case studies, I will show how the proposed approaches allow one to efficiently answer heterogeneous questions, unifying different modeling techniques and promoting interdisciplinarity, modularity, and compositionality. I will then discuss open challenges for compositional systems design optimization, and present my agenda to tackle them.
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- Date & Time: Tuesday, October 10, 2023; 1:00 PM
Speaker: Shaoshuai Mou, Purdue University
MERL Host: Yebin Wang
Research Areas: Control, Dynamical Systems, Robotics
Abstract 
Inverse Optimal Control (IOC) aims to achieve an objective function corresponding to a certain task from an expert robot driven by optimal control, which has become a powerful tool in many applications in robotics. We will present our recent solutions to IOC based on incomplete observations of systems' trajectories, which enables an autonomous system to “sense-and-adapt", i.e., incrementally improving the learning of objective functions as new data arrives. This also leads to a distributed algorithm to solve IOC in multi-agent systems, in which each agent can only access part of the overall trajectory of an optimal control system and cannot solve IOC by itself. This is perhaps the first distributed method to IOC. Applications of IOC into human prediction will also be given.
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- Date: July 9, 2023 - July 14, 2023
MERL Contacts: Karl Berntorp; Scott A. Bortoff; Ankush Chakrabarty; Stefano Di Cairano; Christopher R. Laughman; Diego Romeres; Abraham P. Vinod
Research Areas: Control, Dynamical Systems, Machine Learning, Multi-Physical Modeling, Optimization, Robotics
Brief - MERL researchers presented 9 papers and organized 2 invited/workshop sessions at the 2023 IFAC World Congress held in Yokohama, JP.
MERL's contributions covered topics including decision-making for autonomous vehicles, statistical and learning-based estimation for GNSS and energy systems, impedance control for delta robots, learning for system identification of rigid body dynamics and time-varying systems, and meta-learning for deep state-space modeling using data from similar systems. The invited session (MERL co-organizer: Ankush Chakrabarty) was on the topic of “Estimation and observer design: theory and applications” and the workshop (MERL co-organizer: Karl Berntorp) was on “Gaussian Process Learning for Systems and Control”.
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- Date: June 26, 2023
Where: International Conference on Smart Computing (SMARTCOMP), Vanderbilt University, Nashville, Tennessee
MERL Contact: Philip V. Orlik
Research Areas: Communications, Dynamical Systems, Machine Learning, Multi-Physical Modeling, Signal Processing
Brief - VP & Research Director, Philip Orlik, gave a keynote titled, "Smart Technologies for Smarter Buildings" at the 9th edition of the IEEE International Conference on Smart Computing (SMARTCOMP) focusing on some of the research challenges and opportunities that arise as we seek to achieve net-zero emissions in Smart building environments.
SMARTCOMP is the premier conference on smart computing. Smart computing is a multidisciplinary domain based on the synergistic influence of advances in sensor-based technologies, Internet of Things, cyber-physical systems, edge computing, big data analytics, machine learning, cognitive computing, and artificial intelligence.
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- Date: June 9, 2023
Awarded to: Cristian J. Vaca-Rubio, Pu Wang, Toshiaki Koike-Akino, Ye Wang, Petros Boufounos and Petar Popovski
MERL Contacts: Petros T. Boufounos; Toshiaki Koike-Akino; Pu (Perry) Wang; Ye Wang
Research Areas: Artificial Intelligence, Communications, Computational Sensing, Dynamical Systems, Machine Learning, Signal Processing
Brief - A MERL Paper on Wi-Fi sensing was recognized as a Top 3% Paper among all 2709 accepted papers at the 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2023). Co-authored by Cristian Vaca-Rubio and Petar Popovski from Aalborg University, Denmark, and MERL researchers Pu Wang, Toshiaki Koike-Akino, Ye Wang, and Petros Boufounos, the paper "MmWave Wi-Fi Trajectory Estimation with Continous-Time Neural Dynamic Learning" was also a Best Student Paper Award finalist.
Performed during Cristian’s stay at MERL first as a visiting Marie Skłodowska-Curie Fellow and then as a full-time intern in 2022, this work capitalizes on standards-compliant Wi-Fi signals to perform indoor localization and sensing. The paper uses a neural dynamic learning framework to address technical issues such as low sampling rate and irregular sampling intervals.
ICASSP, a flagship conference of the IEEE Signal Processing Society (SPS), was hosted on the Greek island of Rhodes from June 04 to June 10, 2023. ICASSP 2023 marked the largest ICASSP in history, boasting over 4000 participants and 6128 submitted papers, out of which 2709 were accepted.
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- Date: June 8, 2023
Where: Zoom
MERL Contact: Abraham P. Vinod
Research Areas: Artificial Intelligence, Control, Dynamical Systems, Optimization, Robotics
Brief - Abraham Vinod gave an invited talk at the Electrical and Computer Engineering Department, the University of California Santa Cruz, titled "Motion Planning under Constraints and Uncertainty using Data and Reachability". His presentation covered recent work on fast and safe motion planners that can allow for coordination among agents, mitigate uncertainty arising from sensing limitations and simplified models, and tolerate the possibility of failures.
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- Date: June 30, 2023 - June 2, 2023
Where: San Diego, CA
MERL Contact: Ankush Chakrabarty
Research Areas: Applied Physics, Artificial Intelligence, Control, Data Analytics, Dynamical Systems, Machine Learning, Multi-Physical Modeling, Optimization, Robotics
Brief - Ankush Chakrabarty (researcher, Multiphysical Systems Team) co-organized and spoke at 3 sessions at the 2023 American Control Conference in San Diego, CA. These include: (1) A tutorial session (w/ Stefano Di Cairano) on "Physics Informed Machine Learning for Modeling and Control": an effort with contributions from multiple academic institutes and US research labs; (2) An invited session on "Energy Efficiency in Smart Buildings and Cities" in which his paper (w/ Chris Laughman) on "Local Search Region Constrained Bayesian Optimization for Performance Optimization of Vapor Compression Systems" was nominated for Best Energy Systems Paper Award; and, (3) A special session on Diversity, Equity, and Inclusion to improve recruitment and retention of underrepresented groups in STEM research.
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- Date & Time: Tuesday, April 11, 2023; 11:00 AM
Speaker: Michael Muehlebach, Max Planck Institute for Intelligent Systems
Research Areas: Control, Dynamical Systems, Machine Learning, Optimization, Robotics
Abstract 
The talk will be divided into two parts. The first part of the talk introduces a class of first-order methods for constrained optimization that are based on an analogy to non-smooth dynamical systems. The key underlying idea is to express constraints in terms of velocities instead of positions, which has the algorithmic consequence that optimizations over feasible sets at each iteration are replaced with optimizations over local, sparse convex approximations. This results is a simplified suite of algorithms and an expanded range of possible applications in machine learning. In the second part of my talk, I will present a robot learning algorithm for trajectory tracking. The method incorporates prior knowledge about the system dynamics and by optimizing over feedforward actions, the risk of instability during deployment is mitigated. The algorithm will be evaluated on a ping-pong playing robot that is actuated by soft pneumatic muscles.
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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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- Date & Time: Monday, December 12, 2022; 1:00pm-5:30pm ET
Location: Mitsubishi Electric Research Laboratories (MERL)/Virtual
Research Areas: Applied Physics, Artificial Intelligence, Communications, Computational Sensing, Computer Vision, Control, Data Analytics, Dynamical Systems, Electric Systems, Electronic and Photonic Devices, Machine Learning, Multi-Physical Modeling, Optimization, Robotics, Signal Processing, Speech & Audio, Digital Video
Brief - Join MERL's virtual open house on December 12th, 2022! Featuring a keynote, live sessions, research area booths, and opportunities to interact with our research team. Discover who we are and what we do, and learn about internship and employment opportunities.
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- Date: November 14, 2022
Where: Zoom
MERL Contact: Rien Quirynen
Research Areas: Control, Dynamical Systems, Optimization, Robotics
Brief - Rien Quirynen will give an invited talk at the Electrical and Computer Engineering Department, University of California Santa Cruz on "Real-time Motion Planning and Predictive Control by Mixed-integer Programming for Autonomous Vehicles". The talk will present recent work on a tailored branch-and-bound method for real-time motion planning and decision making on embedded processing units, and recent results for two applications related to automated driving and traffic control.
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- Date: November 11, 2022
MERL Contact: Avishai Weiss
Research Areas: Control, Dynamical Systems, Optimization
Brief - Avishai Weiss will give an invited talk at the William Maxwell Reed Seminar Series, Mechanical and Aerospace Engineering Department, University of Kentucky on "Fail-Safe Spacecraft Rendezvous." The talk will present some recent developments at MERL on guaranteeing safe rendezvous trajectories that avoid colliding with the target in the event of thruster anomalies.
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- Date & Time: Wednesday, October 26, 2022; 1:00 PM
Speaker: Ufuk Topcu, The University of Texas at Austin
MERL Host: Abraham P. Vinod
Research Areas: Control, Dynamical Systems, Optimization
Abstract - Autonomous systems are emerging as a driving technology for countlessly many applications. Numerous disciplines tackle the challenges toward making these systems trustworthy, adaptable, user-friendly, and economical. On the other hand, the existing disciplinary boundaries delay and possibly even obstruct progress. I argue that the nonconventional problems that arise in designing and verifying autonomous systems require hybrid solutions in the intersection of learning, formal methods, and controls. I will present examples of such hybrid solutions in the context of learning in sequential decision-making processes. These results offer novel means for effectively integrating physics-based, contextual, or structural prior knowledge into data-driven learning algorithms. They improve data efficiency by several orders of magnitude and generalizability to environments and tasks that the system had not experienced previously.
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- Date: October 24, 2022
Where: Online, 10/24/2022 9:00am (Eastern time)
MERL Contact: Stefano Di Cairano
Research Areas: Control, Dynamical Systems, Optimization, Robotics
Brief - Dr. Stefano Di Cairano (Senior Team Leader at MERL) has been invited to give a public talk at the first IEEE CSS Day event on the status, challenges, and role of control in autonomous driving.
The talk, titled "The Long Voyage Towards Autonomous Driving, with Control Systems as the Co-Pilot", will review some history of autonomous driving, some of the open challenges that control technology may help address, and the next steps towards full-autonomy. The talk is designed for a non-technical audience, to explain the role and impact of control in automated driving technology.
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- Date: August 25, 2022
MERL Contact: Anthony Vetro
Research Areas: Dynamical Systems, Machine Learning, Multi-Physical Modeling
Brief - MERL researcher Saleh Nabi was interviewed by Globest.com regarding the use of airflow optimization for smarter energy use and disease prevention. The article titled "High Tech Airflow Control for Smarter Energy Use: Reducing costs and improving effectiveness means a lot of tricky math" was recently published and describes how the solutions to complex fluid dynamical equations leads to improved HVAC control.
Globest.com is a trusted and independent team of experts providing commercial real estate professionals with comprehensive coverage and best practices necessary to innovate and build their businesses. More details about Globest can be found here: https://www.globest.com/static/about-us/
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- Date: September 21, 2022
MERL Contacts: Philip V. Orlik; Anthony Vetro
Research Areas: Applied Physics, Artificial Intelligence, Communications, Computational Sensing, Computer Vision, Control, Data Analytics, Dynamical Systems, Electric Systems, Electronic and Photonic Devices, Machine Learning, Multi-Physical Modeling, Optimization, Robotics, Signal Processing, Speech & Audio
Brief - Mitsubishi Electric Research Laboratories (MERL) invites qualified postdoctoral candidates to apply for the position of Postdoctoral Research Fellow. This position provides early career scientists the opportunity to work at a unique, academically-oriented industrial research laboratory. Successful candidates will be expected to define and pursue their own original research agenda, explore connections to established laboratory initiatives, and publish high impact articles in leading venues. Please refer to our web page for further details.
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- Date: September 15, 2022
MERL Contact: Yebin Wang
Research Areas: Control, Dynamical Systems, Robotics
Brief - Yebin Wang, a Senior Principal Research Scientist in MERL's Electric Machines and Devices, is serving as an Associate Editor for the IEEE International Conference on Robotics and Automation (ICRA) 2023.
As the flagship conference of the IEEE Robotics and Automation Society, ICRA will bring together the world's top researchers and most important companies to share ideas and advances in our field.
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- Date: August 25, 2022
Awarded to: Marcus Greiff
MERL Contact: Marcus Greiff
Research Areas: Control, Dynamical Systems, Robotics
Brief - Marcus Greiff, a Visiting Research Scientist at MERL, was awarded one of three outstanding student paper awards at the IEEE CCTA 2022 conference for his paper titled "Quadrotor Control on SU(2)xR3 with SLAM Integration". The award was given for originality, clarity, and potential impact on practical applications of control. The work presents a complete UAV control system design, facilitating autonomous supermarket inventorying without the need for external motion capture systems. A video of the experiments is on YouTube, including both simulations and real-time examples.
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- Date & Time: Tuesday, April 12, 2022; 11:00 AM EDT
Speaker: Sebastien Gros, NTNU
MERL Host: Rien Quirynen
Research Areas: Control, Dynamical Systems, Optimization
Abstract 
Reinforcement Learning (RL), similarly to many AI-based techniques, is currently receiving a very high attention. RL is most commonly supported by classic Machine Learning techniques, i.e. typically Deep Neural Networks (DNNs). While there are good motivations for using DNNs in RL, there are also significant drawbacks. The lack of “explainability” of the resulting control policies, and the difficulty to provide guarantees on their closed-loop behavior (safety, stability) makes DNN-based policies problematic in many applications. In this talk, we will discuss an alternative approach to support RL, via formal optimal control tools based on Model Predictive Control (MPC). This approach alleviates the issues detailed above, but also presents some challenges. In this talk, we will discuss why MPC is a valid tool to support RL, and how MPC can be combined with RL (RLMPC). We will then discuss some recent results regarding this combination, the known challenges, and the kind of control applications where we believe that RLMPC will be a valuable approach.
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- Date & Time: Tuesday, April 5, 2022; 11:00 AM EDT
Speaker: Albert Benveniste, Benoît Caillaud, and Mathias Malandain, Inria
MERL Host: Scott A. Bortoff
Research Areas: Dynamical Systems, Multi-Physical Modeling
Abstract 
Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In our introduction, will briefly explain why and when the approximate structural analysis implemented in current Modelica tools leads to such errors. Then we will present our multimode Pryce Sigma-method for index reduction, in which the mode-dependent Sigma-matrix is represented in a dual form, by attaching, to every valuation of the sigma_ij entry of the Sigma matrix, the predicate characterizing the set of modes in which sigma_ij takes this value. We will illustrate this multimode analysis on example, by using our IsamDAE tool. In a second part, we will complement this multimode DAE structural analysis by a new structural analysis of mode changes (and, more generally, transient modes holding for zero time). Also, mode changes often give raise to impulsive behaviors: we will present a compile-time analysis identifying such behaviors. Our structural analysis of mode changes deeply relies on nonstandard analysis, which is a mathematical framework in which infinitesimals and infinities are first class citizens.
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- Date: July 5, 2022 - July 7, 2022
MERL Contact: Mouhacine Benosman
Research Areas: Control, Data Analytics, Dynamical Systems
Brief - The Benelux meeting is an annual conference gathering of the scientific community of Belgium, the Netherlands, and Luxemburg around systems and control. It is especially intended for PhD researchers and a number of activities are dedicated to them, including plenary talks and a mini-course.
Dr. Benosman has been invited to give the mini-course of the 2022 edition of the conference. This course, entitled 'A hybrid approach to control: classical control theory meets machine learning theory', will be centered around the topic of safe and robust machine learning-based control.
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- Date & Time: Tuesday, December 14, 2021; 1:00 PM EST
Speaker: Prof. Chris Fletcher, University of Waterloo
MERL Host: Ankush Chakrabarty
Research Areas: Dynamical Systems, Machine Learning, Multi-Physical Modeling
Abstract 
Decision-making and adaptation to climate change requires quantitative projections of the physical climate system and an accurate understanding of the uncertainty in those projections. Earth system models (ESMs), which solve the Navier-Stokes equations on the sphere, are the only tool that climate scientists have to make projections forward into climate states that have not been observed in the historical data record. Yet, ESMs are incredibly complex and expensive codes and contain many poorly constrained physical parameters—for processes such as clouds and convection—that must be calibrated against observations. In this talk, I will describe research from my group that uses ensembles of ESM simulations to train statistical models that learn the behavior and sensitivities of the ESM. Once trained and validated the statistical models are essentially free to run, which allows climate modelling centers to make more efficient use of precious compute cycles. The aim is to improve the quality of future climate projections, by producing better calibrated ESMs, and to improve the quantification of the uncertainties, by better sampling the equifinality of climate states.
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- Date & Time: Thursday, December 9, 2021; 1:00pm - 5:30pm EST
Location: Virtual Event
Speaker: Prof. Melanie Zeilinger, ETH
Research Areas: Applied Physics, Artificial Intelligence, Communications, Computational Sensing, Computer Vision, Control, Data Analytics, Dynamical Systems, Electric Systems, Electronic and Photonic Devices, Machine Learning, Multi-Physical Modeling, Optimization, Robotics, Signal Processing, Speech & Audio, Digital Video, Human-Computer Interaction, Information Security
Brief - MERL is excited to announce the second keynote speaker for our Virtual Open House 2021:
Prof. Melanie Zeilinger from ETH .
Our virtual open house will take place on December 9, 2021, 1:00pm - 5:30pm (EST).
Join us to learn more about who we are, what we do, and discuss our internship and employment opportunities. Prof. Zeilinger's talk is scheduled for 3:15pm - 3:45pm (EST).
Registration: https://mailchi.mp/merl/merlvoh2021
Keynote Title: Control Meets Learning - On Performance, Safety and User Interaction
Abstract: With increasing sensing and communication capabilities, physical systems today are becoming one of the largest generators of data, making learning a central component of autonomous control systems. While this paradigm shift offers tremendous opportunities to address new levels of system complexity, variability and user interaction, it also raises fundamental questions of learning in a closed-loop dynamical control system. In this talk, I will present some of our recent results showing how even safety-critical systems can leverage the potential of data. I will first briefly present concepts for using learning for automatic controller design and for a new safety framework that can equip any learning-based controller with safety guarantees. The second part will then discuss how expert and user information can be utilized to optimize system performance, where I will particularly highlight an approach developed together with MERL for personalizing the motion planning in autonomous driving to the individual driving style of a passenger.
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- Date & Time: Thursday, December 9, 2021; 1:00pm - 5:30pm EST
Location: Virtual Event
Speaker: Prof. Ashok Veeraraghavan, Rice University
Research Areas: Applied Physics, Artificial Intelligence, Communications, Computational Sensing, Computer Vision, Control, Data Analytics, Dynamical Systems, Electric Systems, Electronic and Photonic Devices, Machine Learning, Multi-Physical Modeling, Optimization, Robotics, Signal Processing, Speech & Audio, Digital Video, Human-Computer Interaction, Information Security
Brief - MERL is excited to announce the first keynote speaker for our Virtual Open House 2021:
Prof. Ashok Veeraraghavan from Rice University.
Our virtual open house will take place on December 9, 2021, 1:00pm - 5:30pm (EST).
Join us to learn more about who we are, what we do, and discuss our internship and employment opportunities. Prof. Veeraraghavan's talk is scheduled for 1:15pm - 1:45pm (EST).
Registration: https://mailchi.mp/merl/merlvoh2021
Keynote Title: Computational Imaging: Beyond the limits imposed by lenses.
Abstract: The lens has long been a central element of cameras, since its early use in the mid-nineteenth century by Niepce, Talbot, and Daguerre. The role of the lens, from the Daguerrotype to modern digital cameras, is to refract light to achieve a one-to-one mapping between a point in the scene and a point on the sensor. This effect enables the sensor to compute a particular two-dimensional (2D) integral of the incident 4D light-field. We propose a radical departure from this practice and the many limitations it imposes. In the talk we focus on two inter-related research projects that attempt to go beyond lens-based imaging.
First, we discuss our lab’s recent efforts to build flat, extremely thin imaging devices by replacing the lens in a conventional camera with an amplitude mask and computational reconstruction algorithms. These lensless cameras, called FlatCams can be less than a millimeter in thickness and enable applications where size, weight, thickness or cost are the driving factors. Second, we discuss high-resolution, long-distance imaging using Fourier Ptychography, where the need for a large aperture aberration corrected lens is replaced by a camera array and associated phase retrieval algorithms resulting again in order of magnitude reductions in size, weight and cost. Finally, I will spend a few minutes discussing how the wholistic computational imaging approach can be used to create ultra-high-resolution wavefront sensors.
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- Date & Time: Tuesday, November 16, 2021; 11:00 AM EST
Speaker: Thomas Schön, Uppsala University
MERL Host: Karl Berntorp
Research Areas: Dynamical Systems, Machine Learning
Abstract 
While deep learning-based classification is generally addressed using standardized approaches, this is really not the case when it comes to the study of regression problems. There are currently several different approaches used for regression and there is still room for innovation. We have developed a general deep regression method with a clear probabilistic interpretation. The basic building block in our construction is an energy-based model of the conditional output density p(y|x), where we use a deep neural network to predict the un-normalized density from input-output pairs (x, y). Such a construction is also commonly referred to as an implicit representation. The resulting learning problem is challenging and we offer some insights on how to deal with it. We show good performance on several computer vision regression tasks, system identification problems and 3D object detection using laser data.
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