Aras Bacho

Dr. Aras Bacho is a Postdoctoral Research Associate in the Computing and Mathematical Sciences Department within the Division of Engineering and Applied Science at the California Institute of Technology (Caltech), where he works with Professor Houman Owhadi. His research spans mathematical analysis, partial differential equations, and machine learning applications.

Dr. Bacho completed his PhD in Partial Differential Equations at the Technical University of Berlin with a thesis titled "On the Nonsmooth Analysis of Doubly Evolution Inclusions of First and Second Order with Applications" under the supervision of Prof. Dr. Etienne Emmrich. He also holds M.Sc. degrees in Mathematics from both the Technical University Berlin and Université Pierre et Marie Curie in Paris (through an ERASMUS+ scholarship), as well as a B.Sc. in Technomathematics from the Technical University Berlin.

Dr. Bacho's research interests focus on the intersection of mathematical analysis and machine learning. His work explores partial differential equations, nonsmooth analysis, physics-informed neural networks, and applications in robotics and computational physics. His research bridges theoretical mathematics with practical applications in artificial intelligence and engineering systems. He has developed novel approaches to physics-informed machine learning and has made contributions to the mathematical foundations of scientific machine learning.

Dr. Bacho's publications demonstrate a strong trajectory from theoretical mathematical analysis toward increasingly applied work in scientific machine learning. His recent work shows particular interest in physics-informed neural networks, equation discovery, and the mathematical foundations of AI reliability. He has published on topics ranging from classical PDE theory to cutting-edge applications of deep learning in scientific computing, with a focus on mathematical rigor and practical applicability.

• 2008: First prize in the Nationwide Mathematics Competition in Germany (Bundeswettbewerb Mathematik)
• 2009: DPG Prize for special achievements in physics issued by the German Physical Society
• 2012: Perfect score in the Math Advent Calendar organized by the DFG Research Center MATHEON
• 2014-2015: Erasmus+ Scholarship for studies at Université Pierre et Marie Curie
• 2017: PhD-Scholarship issued by TU Berlin (4 Months)
• 2021-present: Mentoring Program for young researchers

Dr. Bacho has presented his work at numerous international conferences including the Workshop on Control of Self-Organizing Nonlinear Systems, the Hausdorffschool on Modeling and analysis of evolutionary problems, and the International Council for Industrial and Applied Mathematics (ICIAM) 2023. His research has been supported by various grants including his PhD scholarship from TU Berlin and participation in mentoring programs for young researchers. He collaborates with researchers across mathematics, computer science, and engineering disciplines.

Dr. Bacho is actively involved in the scientific machine learning community, collaborating with researchers at Caltech and beyond. His work at the intersection of mathematical analysis and AI places him at the forefront of scientific machine learning research, with particular emphasis on the mathematical foundations of physics-informed neural networks and the reliability of AI systems for scientific applications.