Research

My research interests are in the fields of machine learning and scientific computing. I am interested in the development of machine learning methods for science, with a focus on interpretable AI and healthcare applications.

AI for Science

I am passionate about using machine learning to advance scientific research. In particular, I have been successful in applying these techniques to the field of cardiac electrophysiology. State-of-the-art methods for non-invasive imaging of cardiac electrical activity often require recordings from multiple locations on the torso and the use of costly medical imaging procedures. My work aims to explore whether machine learning can be used to reconstruct electroanatomical maps at clinically relevant resolutions using only standard 12-lead electrocardiograms (ECGs) as input. To this end, I have generated a dataset of over 16000 detailed cardiac simulations and trained neural network models to capture spatial and temporal correlations in ECG signals. The method was able to accurately reconstruct the phenotypical patterns of activation and the potential morphology. This work has the potential to non-invasively stratify patients using metrics that are typically only available through invasive clinical procedures.

Currently, I am working on using machine learning to accelerate the process of antibody engineering. Antibodies are a crucial class of therapeutic proteins that are used to treat a wide range of diseases. However, developing new antibodies is a lengthy and expensive endeavor. By applying machine learning, I hope to find ways to make this process more efficient. I am applying the latest advances in deep learning, like transformers and GPT-like models, to produce models that can suggest mutations to improve the binding affinity of antibodies. The goal is to develop a model that can be used to guide the design of new antibodies and accelerate the process of antibody engineering.

Interpretability in AI

I am interested in developing interpretable machine learning methods and applying them to real-world problems. My focus is on finding simple, interpretable models that can accurately capture the underlying patterns in the data, which aligns with the core principles of the scientific method. This line of research, known as symbolic regression in mathematics, seeks to produce parsimonious, simple models that can generalize well even in small data regimes. I have been working on developing symbolic regression methods using deep learning in combination with advanced techniques like evolutionary search. In contrast to neural networks, our deep learning-aided symbolic regression algorithms are able to generalize well in small data regimes. For example, when predicting the sequence of harmonic numbers $H_n = \sum_{k=1}^n \frac{1}{k}$, we found that the error of our predictors was less thatn 0.0001% and were able to recover the Euler-Mascheroni constant $\gamma$ in the process.

I have applied these methods to a variety of problems, including discovering interpretable controllers for classical reinforcement learning environments. The resulting policies are interpretable and maintain a high level of accuracy. The performance of these policies can be attributed to the unreasonalble effectivenes of mathematics to capture patterns in physical and dynamical systems. Overall, my research focuses on improving the interpretability and simplicity of machine learning models, with the aim of advancing the field and finding practical applications. Current research focus on developing decision trees as controllers for reinforcement learning agents.

Scientific Computing

My research focuses on developing numerical methods for the simulation of complex systems, with a particular emphasis on high performance computing. I have worked on developing methods for simulating cardiac electrophysiology and fluid-structure interaction problems. The latter involves modeling the interaction between a deformable thin-walled structure and an incompressible fluid flow. I have proposed new classes of explicit coupling schemes using fitted meshes that combine Robin-consistency with projection-based time-marching or second-order time-stepping. I have also studied the stability and error estimates of these methods and compared them to existing state-of-the-art approaches. Additionally, I have explored the use of Nitsche’s method with cut elements for spatial discretization in unfitted mesh formulations, and developed new classes of splitting schemes that exploit Robin-consistency in the unfitted framework. This work has the potential to advance the field of numerical methods and enable the development of digital twins for complex systems.

I believe that the combination of scientific computing and machine learning has the potential to greatly advance scientific and engineering fields. Major implications for fields such as health science and robotics are already being explored. For example, a digital twin of the human body could be used to predict the onset of diseases and develop personalized treatments, or a digital twin of a robot could be used to predict the failure of a component and develop preventive maintenance strategies. This research effort requires the development of accurate numerical methods that are also computationally efficient since they have to integrated within machine learning loops that are typically data-hungry. I am currently working on developing new numerical methods for the simulation of complex systems, with a particular emphasis on high performance computing.