AIMdyn, Inc.

Employee Spotlight: Dr.Maria Fonoberova We are delighted to spotlight Maria, our esteemed Director of Research at AIMdyn, who has been an invaluable member of our team since 2008. Maria earned her B.S. in Applied Mathematics from Moldova State University in 2005 and went on to receive her Ph.D. in Mathematics and Physics from the Academy of Sciences of Moldova in 2008. With over 15 years of experience in big data analytics and the spectral analysis of dynamical systems, she has played a key role in leading successful R&D programs for government clients as both a Principal Investigator and Project Manager. Her research interests span dynamical systems, Koopman operator techniques, artificial intelligence, and agent-based models. Outside of work, Maria cherishes spending time with her family, traveling, and reading. We are proud to have her drive innovation and excellence at AIMdyn. #EmployeeSpotlight #MachineLearning #Innovation #Teamwork #Koopman #DataAnalytics #Research #DynamicSystems

Happy Presidents' Day from our team at AIMdyn, Inc. May this day inspire us to continue striving for innovation, excellence, and progress in all our endeavors. Wishing everyone a reflective and inspiring Presidents' Day. #PresidentsDay #Leadership #Innovation #AimdynInc

We are thrilled to highlight our publication, "Koopman Learning with Episodic Memory," now available in Chaos: An Interdisciplinary Journal of Nonlinear Science. This work addresses a significant challenge in modeling complex, non-autonomous dynamical systems: the tendency of traditional Koopman models to overlook past data to prevent mixing distinct dynamical regimes. As co-author William Redman explains: "Koopman operator theoretic methods have become increasingly applied to the prediction of complex, non-autonomous dynamical systems. While capable of good performance, these Koopman models often explicitly forget data in the past to avoid the mixing of distinct dynamical regimes. When the underlying time-series contains repeated structure, this temporally-local approach can prevent these recurrent patterns from being leveraged to improve forecasting. To mitigate this, we introduce a framework—Koopman learning with episodic memory—with which to identify when the currently observed dynamics are similar to those observed at a previous point in time, and to use such matches to make more informed predictions. A numerical implementation of Koopman learning with episodic memory demonstrates large improvements in prediction accuracy on synthetic and real-world data sets, and opens new directions for future research." This innovative framework enhances prediction accuracy by recognizing and utilizing recurrent patterns in time-series data, marking a significant advancement in the field of dynamical systems. For a deeper dive into our methodology and findings, read the full paper here: https://lnkd.in/gCYDecmd #KoopmanOperator #DynamicalSystems #MachineLearning #DataScience #ResearchInnovation

?? Presentation Spotlight: Soft Robots & Koopman Operator Framework One of our AIMdyn, Inc. researchers, Ervin Kamenar, recently presented on soft robots that are inspired by natural structures. These systems enable safe human-machine interactions and are particularly useful in medical applications, such as robotic rehabilitation. As he explained: "One of the key challenges is their highly complex modeling and control, which was recently addressed in the publication: https://lnkd.in/garRmnTg. The described methodology fully relies on the Koopman operator framework, proving to be a powerful technique for modeling and controlling highly complex structures such as nonlinear soft robots. This technology not only enables precise navigation of the robot's tip within its reachable space but also facilitates highly dynamic movements, laying the foundation for the future development of advanced soft robots." This innovative approach is pushing the boundaries of robotics and AI-driven control systems. What are your thoughts on the future of soft robotics? Join the discussion in the comments! #SoftRobotics #KoopmanOperator #RoboticsInnovation #AIResearch #MedicalTechnology #ScienceAndEngineering #Aimdyn

Presentation Highlight: "Development of magnetic-imaging platform for biological assays" Last month our team member Isaac Shelby gave a presentation on his graduate work on developing a new imaging system for quantitative, single molecule, biological measurements. With advances in the field of quantitative, single-molecule biological measurements, it has become increasingly interesting to study systems that have a rotational or orientation component. Traditional imaging techniques can (and have been) modified to probe these additional degrees of freedom, but have limitations. Using the spin-optical readout of nitrogen vacancy centers in a diamond chip, it is possible to measure micro-Tesla magnetic fields generated by ferromagnetic beads of <50 nm; this creates an unbleachable probe of position and orientation. Due to the small magnitude of the signal and spatial distribution, care must be taken to eliminate the impact of slight variations in diamond structure and local magnetic field across the diamond imaging chip. We hope to see more research like this in the future, if you have any questions start a discussion down below ?? #research #scientificstudy #imaging #biotech #presentation

Presentation Highlight: "Quantitative Harris Theorems on General State Spaces" Last month Chris DuPre gave an intriguing presentation on the development of quantitative mixing theorems for general state Markov chains. He explained how Markov chains form a powerful model for the evolution of random systems and have a wide range of applications (including PageRank, the algorithm behind Google's search engine). For any given Markov chain, we are often interested in a quantity known as the mixing rate which describes how quickly the chain relaxes to a steady state. In the finite state space setting, many beautiful theorems exist to prove the existence of mixing rates and estimate their value. In the general state space, the tools that exist are often far more delicate. We introduce the general theory, as well as a novel condition describing the quantitative dependence of the mixing rate on more easily verifiable conditions. For more exciting topics and information relating to data analysis, give us a follow and support our team! #Dataanalysis #Presentation #Research #Science #MarkovChain #Markov

A nice application of #Koopmanoperator theory to galactic dynamics here: https://lnkd.in/g23bRA85

Last May, we held a workshop in Otranto, Italy, connecting Koopman operator theory and climate science. Here is a writeup on it https://lnkd.in/gqNe79Ax #AI #Koopmanoperator #ML #dynamicalsystems #chaostheory

?? Paper Spotlight ?? Today, let’s dive into the groundbreaking work of Alexander Krolicki, S. Sutivani, and U. Vaidya in their paper, “Koopman-based Policy Iteration for Robust Optimal Control”, presented at the 2022 American Control Conference in Atlanta. In the 1960s, pioneers like Pontryagin, Berkovitz, and LaSalle laid the foundation for one-player differential games, while von Neumann and Morgenstern introduced game theory for two-player scenarios. Rufus Isaacs’ 1965 seminal work, “Differential Games,” provided practical solutions for these complex problems, thanks to his collaboration with Professor Bernard Koopman. Isaacs credited Koopman for his innovative thinking, which was crucial for the development of his theories. Fast forward to today, Koopman’s legacy lives on through the Koopman Operator, a concept he introduced in 1931. It took nearly eight decades to develop methods for computing this operator using sampled data, and now, 91 years later, it’s revolutionizing differential games. The paper under review presents a novel approach to solving two-player zero-sum differential games using the Koopman operator. This method combines data-driven and model-based algorithms to approximate the optimal value function, offering robust control solutions for complex nonlinear systems. Just three years after its publication, this paper has already been cited by leading researchers from the National Security Directorate, PNNL, and AFRL in the Journal of Computational Physics. Their work, “Operator-Theoretic Methods for Differential Games,” builds on these novel contributions, highlighting the paper’s pioneering impact. We are incredibly proud of our team member's contribution to Koopman research, if you are interested feel free to join the conversation and share your thoughts on these advancements! #publication #paper #research #koopman #scientificpaper

?? Paper Spotlight ?? Today, let’s dive into the groundbreaking work of Alexander Krolicki, S. Sutivani, and U. Vaidya in their paper, “Koopman-based Policy Iteration for Robust Optimal Control”, presented at the 2022 American Control Conference in Atlanta. In the 1960s, pioneers like Pontryagin, Berkovitz, and LaSalle laid the foundation for one-player differential games, while von Neumann and Morgenstern introduced game theory for two-player scenarios. Rufus Isaacs’ 1965 seminal work, “Differential Games,” provided practical solutions for these complex problems, thanks to his collaboration with Professor Bernard Koopman. Isaacs credited Koopman for his innovative thinking, which was crucial for the development of his theories. Fast forward to today, Koopman’s legacy lives on through the Koopman Operator, a concept he introduced in 1931. It took nearly eight decades to develop methods for computing this operator using sampled data, and now, 91 years later, it’s revolutionizing differential games. The paper under review presents a novel approach to solving two-player zero-sum differential games using the Koopman operator. This method combines data-driven and model-based algorithms to approximate the optimal value function, offering robust control solutions for complex nonlinear systems. Just three years after its publication, this paper has already been cited by leading researchers from the National Security Directorate, PNNL, and AFRL in the Journal of Computational Physics. Their work, “Operator-Theoretic Methods for Differential Games,” builds on these novel contributions, highlighting the paper’s pioneering impact. We are incredibly proud of our team member's contribution to Koopman research, if you are interested feel free to join the conversation and share your thoughts on these advancements! #publication #paper #research #koopman #scientificpaper