Applied Mathematics

Juan Toscano is a Ph.D. student in the Division of Applied Mathematics at Brown University, working under the guidance of Professor George Karniadakis. Juan's research focuses on developing and applying advanced machine learning techniques, particularly in scientific machine learning (SciML). He is working on creating reliable and stable methods for understanding complex physical systems that are challenging to analyze through traditional approaches. For instance, Juan's work on cerebrospinal fluid dynamics has provided insights into in-vivo pressure gradients and wall shear stress in perivascular spaces, shedding light on mechanical signaling in the brain. His contributions to turbulence research have enabled the inference of hidden temperature fields from experimental velocity data, bridging experimental and computational fluid dynamics.

Before joining Brown, Juan earned his Bachelor’s degree in Mechanical Engineering from the Universidad de las Fuerzas Armadas ESPE in Ecuador. As an undergraduate, he collaborated remotely with the University at Buffalo to apply machine learning techniques to model advanced manufacturing systems. These formative experiences inspired his current focus on physics-informed machine learning (PIML), artificial intelligence velocimetry (AIV), and specialized optimization methods for SciML applications.

Juan’s research includes designing efficient architectures such as Chebyshev Kolmogorov-Arnold Networks (cKANs) and optimization techniques like Residual-Based Attention with Resampling (RBA-R), which have advanced the predictive capabilities of PIML algorithms. By combining mathematics, fluid mechanics, and computational methods, he strives to bridge the gap between theoretical innovation and practical application.

Beyond his academic pursuits, Juan values collaboration and actively contributes to the research community by sharing knowledge and learning from others. 

More about his work and contributions can be found on his profiles:
Google Scholar: https://scholar.google.com/citations?user=XNvLUKwAAAAJ&hl=en

LinkedIn: https://www.linkedin.com/in/juan-diego-toscano-908011ab/
ResearchGate: https://www.researchgate.net/profile/Juan-Toscano-4

GitHub: https://github.com/jdtoscano94

Originally from Ecuador, Juan draws inspiration from his diverse background and enjoys exploring new perspectives in science and life. In his free time, he enjoys cycling and playing piano, balancing the challenges of his academic journey with personal growth and reflection.