About me
Welcome to my academic website!
I am Manuela Bastidas, a researcher and faculty member in the Department of Mathematics at the Universidad Nacional de Colombia, Medellín. My work focuses on the development and analysis of numerical methods for partial differential equations. I am passionate about leveraging mathematical modeling and computational techniques to solve real-world problems in energy, environment, and science.
My research interests lie in areas such as finite element methods, multiscale methods, and physics-informed neural networks. I actively publish my research in leading academic journals and conferences, aiming to contribute to the advancement of knowledge in computational mathematics and its applications.
... Explore this site to learn more about my research projects, publications, teaching activities, and opportunities for collaboration.
My research interests lie in areas such as finite element methods, multiscale methods, and physics-informed neural networks. I actively publish my research in leading academic journals and conferences, aiming to contribute to the advancement of knowledge in computational mathematics and its applications.
... Explore this site to learn more about my research projects, publications, teaching activities, and opportunities for collaboration.
Currently obsessed with...
- AI that knows the laws of physics. Physics-Informed Neural Networks — where deep learning meets rigorous mathematics.
- One model. Every scale. Multiscale methods for flow and transport, from the pore to the reservoir.
- Error is not optional. A posteriori estimation: because knowing your mistake is half the solution.
- Parallel by design. Domain decomposition for solvers that scale with the problem.
- Equations in the wild. Industrial applications: heat transfer, 3D printing, crop diagnostics.
- Classical meets quantum. Hybrid quantum-neural networks for the next generation of scientific computing.