When the present determines the future, but the approximate present does not approximately determine the future. Edward Lorenz
About Me
Hello! I’m Mario Daniel Panuco. I hold an M.S. in Scientific Computing and Applied Mathematics from UC Santa Cruz, following a B.S. in Computer Science Engineering.
I’m interested in mathematical and computational models of complex, high-dimensional systems: physical fields, neural and biological dynamics, and the numerical methods we use to reason about them.
I’m especially drawn to neural operators: models that learn maps between fields and can serve as fast surrogates for partial differential equations. Particularly, whether a numerical model remains useful under rollout (not just single-step prediction), represents multiple spatial scales, handles uncertainty honestly, and can support control or inference.
Interests
- Neural operators and SciML — wavelet and spectral representations, operator approximation, multiscale dynamics, and long-horizon evaluation for PDE surrogates.
- Physics, digital twins, and control — learned state-transition models for real-time feedback control, with tokamak magnetic-field shaping as a motivating example.
- Inverse problems — computational imaging, wave reconstruction, and differentiable forward models for inference.
- Computational neuroscience — inverse electrophysiology, neural recordings, and Mori–Zwanzig coarse-graining as a way to build reduced models of partially observed biological dynamics.
- Computational biology — computational organoids, genomics, and other biological systems where applied mathematics and scientific machine learning can connect high-dimensional measurements to interpretable mechanisms.
- Complex dynamics — chaotic PDEs, coarse-graining, and evaluation methods that remain meaningful after pointwise trajectories diverge.
- Scientific software — GPU computing, numerical experimentation, and frameworks to accelerate scientific exploration across scientific domains.
Elsewhere: /projects and /teaching.