Computational scientist · PhD candidate

Numerical methods and machine learning for problems governed by physics.

I develop efficient, mathematically grounded deep-learning methods for partial differential equations, with applications to inverse problems in computational oncology. Marie Skłodowska-Curie Doctoral Fellow at the University of Pavia, within the IN-DEEP European Doctoral Network.

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Scientific machine learning

Neural PDE solvers, physics-informed training, optimisation of neural networks.

Numerical PDEs

Finite elements and isogeometric analysis, discretisation and error analysis.

Inverse problems & UQ

Bayesian inversion and model calibration with neural surrogates.

Numerical linear algebra

Low-rank methods, Riemannian optimisation, randomised preconditioning.

Open to collaborations — in research and industry

I work with research groups and with companies that need reliable computational tools: from the mathematical model to efficient, tested code.

ivan.bioli@gmail.com Download CV

For companies

Consulting and project work on simulation, surrogate modelling, optimisation and machine learning for engineering and scientific problems.

For research groups

Joint projects on numerical methods for PDEs, scientific machine learning, inverse problems and uncertainty quantification.

Selected projects

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Industry

Reinforcement learning for Formula 1 race strategy

Internship at the Alfa Romeo F1 Team ORLEN, improving an AI agent that recommends live race-strategy decisions during Grands Prix.

Application · Computational oncology

Uncertainty-aware Bayesian inversion for tumor growth

Calibrating tumor-growth PDE models to patient data with quantified uncertainty, made tractable by a latent-dynamics neural surrogate.

Paper in preparation

Research · Software

Scalable natural gradient descent for neural PDE solvers

Making natural gradient training of physics-informed neural networks fast, using matrix-free solvers with randomized low-rank preconditioning.

To appear in Computer Methods in Applied Mechanics and Engineering

Recent publications

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2026

Riemannian optimization on low-rank tensor train manifolds for the Gross–Pitaevskii equation

I. Bioli, C. Marcati, M. Rakhuba · arXiv preprint

Project arXiv

2025

Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra

I. Bioli, C. Marcati, G. Sangalli · Computer Methods in Applied Mechanics and Engineering (to appear)