Research
Engineering:
Live long ChatGPT...
Welcome to my homepage!
I am a scientist with a background in engineering, approaching my work with a practical orientation. In the realm of engineering, my primary focus is understanding the three-dimensional world that surrounds us. Essentially, I am intrigued by the idea of modeling our environment to enhance, analyze, and comprehend it—a concept akin to a "Digital Twin." My professional journey commenced with the mathematical modeling of an interferometer signal from a KLA tool named WaferSight, which measured the polished surfaces of silicon wafers. This involved the reconstruction of spatial surfaces from noisy data. I employed OpenCL for swift algorithm execution, crucial in a production environment.
My evolution in this field led me to delve into computer vision, particularly 3D techniques. At Datalogic, I contributed to algorithms ensuring the accurate functioning of a laser scanner, specifically the DM3610. Joining an established team, I learned conventional engineering approaches such as point cloud manipulation using filters, storage boxes, convex hulls, and minimal bounding boxes. Additionally, I incorporated machine learning tools to tackle similar challenges, particularly when traditional engineering methods proved cumbersome—such as separating objects on a high-speed belt.
Another significant project involves the analysis of Intel's RealSense 3D cameras for object identification purposes. While primarily engaged in algorithmic development using Matlab, I also participate in creating a system for reading data from three cameras, integrating it with regular RGB cameras. This project employs ROS on Ubuntu and utilizes PCL, offering a comprehensive experience in data acquisition.
Furthermore, I developed intricate algorithms to detect shapes (planes, circles, etc.) in preparation for OCR and barcode reading. These algorithms involve geodesic equations, noisy point cloud approximations, and fusion with grayscale/RGB cameras. Overseeing the work of a team member developing machine learning algorithms, we utilized Tensorflow and successfully created a prototype for shape detection.
Post my tenure at Datalogic, I immersed myself in pure machine learning development. At the startup LatentAI, I gained expertise in simplifying and speeding up ML models. This included hands-on experience with "small" models and knowledge of edge deployment on small devices, as well as processes like quantization. Transitioning to the industrial world, I applied this knowledge at PTC in SaaS development.
My role at PTC is both challenging and captivating. I focus on developing ML models to address various challenges related to the simulation and optimization of mechanical engineering problems. Initially, I worked on simulation run-time estimation using basic data. Subsequently, our focus shifted to estimating simulation results, leading to a collaboration with DeepMind on optimization estimation—an intriguing and challenging project. The main tools I utilized for this endeavor are graph neural networks. In essence, my role is a dream job, where I use ML tools to predict simulation outcomes in the realm of physics, and I am also involved in developing MLOPs for this project.
Academic world:
Research Interests:
System theory, Operator theory, (Inverse) scattering theory, Completely integrable PDEs.
I am collecting CI PDEs (in order to classify them later via vessel parameters). Please send me (andreymath@gmail.com) any equation that does not appear on the list of known CI equations (known to me :-)!).
Few words about my research:
I have developed a method to solve a special type of partial differential equations called Completely Integrable (CI). As in the classical case, the (inverse) scattering theory is at the heart of this solution, but I have generalized it and inserted into a formalism of a “realization theory”. Initially, in order to understand a physical object, one could study how the light (or an electromagnetic wave) is scattered if pointed on this object. It was discovered in 60th that it is possible to fully recover the object from its “scattering data” and a mathematical arsenal was developed in order to solve so called Schrodinger 1-dimensional equation. Parameters of this equation, which become a serious obstacle nowadays, must be decreasing or the method of the inverse scattering does not work. In my method, the parameters are arbitrary (analytic) which enables to study much more difficult problems of this theory. Moreover, this method can be generalized to much wider families of linear differential equations.
Linear differential equations are at the heart of estimation theory and signal processing. These last two pairs of words could be considered as the most difficult problems of the modern engineering. They are extremely complicated and only linear cases are fully studied, because we have enough mathematics for it. Non linear estimation and signal processing is the most important and complicated problem in engineering. A toy, non linear equation, on which everyone checks his tools is so called Korteweg-de Vries equation. The method of inverse scattering solution for this equation was developed in 1967, and few years later many more completely integrable PDEs were shown to match the scheme of the inverses scattering solution. All these ideas found its implementation in engineering on different levels: for example, Non Linear Schrodinger equation is at the heart of the fiber optics; Boussinesq equation is at the basis of shallow water waves. There are many more examples, related to physics (electromagnetic fields, quantum theory, etc)
In my research it was shown that already these three important equations (appearing in Wikipedia): Korteweg-de Vries, Non Linear Schrodinger, Boussinesq are solved using my method for wider families of parameters (again, in the original setting they were usually rapidly decreasing). This enables to solve at least the indicated equations in many circumstances. Moreover, the theory itself is just at its first stage and few more equations were revealed and studied, using this method. Worth to mention that equations of the KdV hierarchy were created by this method too.
See vessels link for more details on the mathematics behind this method.