Statement of Research Interest

Statement of Research Interest

Maurice Filo Department of Mechanical Engineering University of California, Santa Barbara (UCSB)

I am a Ph.D. candidate at the department of mechanical engineering at UCSB. My research interests revolve around control/estimation theory and distributed dynamical systems in deterministic and stochastic environments. Particularly, my experience in these areas range from analysis to control and from theory to applications. The multidisciplinary nature of my field of study encouraged me to obtain two master's degrees in both electrical and mechanical engineering, which allowed my research to span a wide spectrum of topics and applications. I strongly believe that multidisciplinary research is highly rewarding. In particular, touching upon various research topics often leads to new ideas that eventually correlate to one another.

Research on Computationally Efficient Cochlear Modeling As a pianist, I was always fascinated by the auditory system of humans from the ear to the auditory cortex in the brain. When I started my master's program in electrical engineering at the American University of Beirut (AUB), I found myself spending much time researching about the physics of hearing. Looking at the ear from an engineering perspective, rather than medical, quickly captured my interest after realizing that the outstanding complexity of the ear, as an engineered device, is still not very well understood. As a result, my work focused on understanding how the ear works. This led to my master's thesis and a published journal paper where I applied a control-theoretical framework to develop computationally efficient biomechanical models of the cochlea. I used a model order reduction technique to carry out fast simulations of cochlear response to audio signals. This is particularly useful for psychoacoustic audio signal processing which is a computationally tedious process if no severe approximations are carried out.

Research on Capturing the Style of Piano Composers During my master's program at AUB, I enrolled to a class on pattern recognition. As a course project, I worked on understanding the patterns that encode the style of piano composers. After I finished my master's program and came to UCSB to earn my Ph.D, I continued my work, in collaboration with a colleague and Professor Mariette Awad at AUB. We published a journal paper on capturing the style of piano composers using n-grams and deep learning techniques. This work allowed us to develop and implement an algorithm that predicts, with a very high accuracy, the composer of a musical piece that is not present in the learning database. This takes musicians one step further in uncovering the musical structures that distinguish for example Chopin from Beethoven.

Research on Various Topics on Cochlear Modeling When I came to UCSB, I pursued my research in cochlear modeling by looking at the cochlea as a distributed dynamical system. This also led to a second master's thesis that addresses several topics in cochlear modeling. Particularly, I applied various concepts from computational science, control theory and dynamical systems to develop a general biomechanical model of the cochlea that (1) separates the computational aspects from the analysis of the dynamics and (2) encompasses a wider modeling class via the use of spatially distributed operators. In addition, I employed perturbation theory and dynamic mode decomposition to study the instabilities that may occur in the ear in a deterministic setting.

Research on Structured Stochastic Uncertainty As I was investigating possible sources of instabilities in the cochlea, I asked the following question:

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(Q): What are the effects of stochastic perturbations in the ear? The cochlea is a remarkably sensitive device capable of sensing a very wide range (in magnitude and frequency) of audio signals . As a biological system, it is naturally susceptible to stochastic perturbations. It seemed convincing that stochastic uncertainties perturbing such a sensitive device will cause instabilities. As I did my research on continuous-time dynamical systems with stochastic perturbations that enter the dynamics multiplicatively, I realized that there is a gap in the control literature in this area. This raised many questions regarding different stochastic interpretations (such as It?o and Stratonovich). Answering those questions led us to a journal and a conference paper (to be submitted soon) that borrows concepts from the statistics literature to develop a theory for structured stochastic uncertainty in continuous-time dynamical systems. The adopted approach treats the dynamics from a purely input-output approach, rather than the more common state space approach. This approach allowed us to develop new methodology for "stochastic block diagrams" that are favored in the control theory community. Both It?o and Stratonovich interpretations were treated. I am also currently in the process of writing a paper that extends this theory to spatially circulant distributed systems.

Research on Cochlear Instabilities The question (Q) that I asked led to a new theoretical result that helps fill a gap in the literature. The exciting part is applying the developed theory to study the instabilities that arise in the ear due to stochastic perturbations. This led to a conference paper that I presented in Melbourne, Australia at the Conference on Decision and Control (CDC 2017). Furthermore, I submitted a more detailed version as a journal paper to the Journal of Acoustical Society of America (JASA). In that paper, I show, using our developed theory, that stochastic perturbations give rise to instabilities in the ear. This models and explains one source of tinnitus which is still not well understood by biologists. Understanding the source of tinnitus certainly takes us a step forward in the therapeutic direction. As a matter of fact, part of my current research is directed towards using stochastic optimal control theory to suppress tinnitus.

Research on Mobile Sensors in Distributed Environments Another interesting problem that I worked on marries estimation and control theory. Consider an unknown vector field (such as temperature, flow, concentration...) that is dynamically evolving in a stochastic, spatially distributed environment. The ultimate goal is to use mobile sensors efficiently to estimate the unknown field. In fact, this can be seen as a double minimization problem where the objective is to minimize the minimal estimation error. This problem is not new; however I noticed in the literature that engineers tend to solve such problems by "hacking" their way to the solution which is very useful in many scenarios. Nonetheless, my interest revolves around developing a unified mathematical framework for such problems by investing more time on the problem statement rather than immediately going in the direction of finding a solution. This led to a paper I presented in Seattle at the American Control Conference (ACC 2017), where I formulate the problem in a deterministic optimal control setting. In this work, I consider unknown temperature fields described by partial differential equations with unknown boundary conditions. The available sensors that collect the measurements are of two types: pointwise and tomographic sensors. Pointwise sensors measure at single points, whereas tomographic sensors (less addressed in the literature) measure line integrals. Particular tomographic sensing schemes can be implemented using acoustic tomography where the time-of-flight of ultrasonic signals between transceivers are utilized to estimate unknown temperature fields. Future research regarding this topic is directed towards using the same methodology on vector fields such as flows described by the celebrated Navier-Stokes equations.

Research on Numerical Methods in Optimal Control The mobile sensors problem produced a large scale deterministic optimal control problem in a spatiotemporal environment. This led to further research on effective numerical methods to solve such problems. Throughout my research on numerical methods in optimal control, I was interested to look at optimal control problems as regular optimizations but in function space. This introduced new insights and geometrical interpretations for a class of recently developed numerical methods. This led to a paper that I will present in Wisconsin at ACC 2018.

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