2025-07-23 –, Main Room 3
Forecasting tumor growth is critical for optimizing treatment, yet traditional models like Gompertz and Bertalanffy equations struggle with patient-specific variability. We leverage Universal Differential Equations (UDEs) and Neural ODEs, integrating Scientific Machine Learning (SciML) to replace rigid terms with adaptive neural networks. This enables real-time learning from patient data, uncovering hidden dynamics beyond classical models to improve clinical outcomes.
Accurately predicting tumor growth is crucial for understanding cancer development and creating effective treatment strategies. Traditional mathematical models that are based on Ordinary Differential Equations (ODEs), such as the Gompertz and Bertalanffy equations, have been widely used to describe tumor growth. While they provide a theoretical foundation, they often fail to account for variations in real-world data. In experimental settings, tumor growth is influenced by a range of factors, including its microenvironment, the presence/ absence of chemotherapy, genetics, immune system response, etc. As a result, ODE models struggle to capture the full complexity of tumor progression.
In order to overcome these limitations, we are using a Scientific Machine Learning (SciML) approach. We leverage Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs) to improve traditional models by learning directly from experimental tumor volume data. Our implementation uses several Julia packages built for SciML applications, such as DifferentialEquations.jl for numerically solving ODEs, DiffEqFlux.jl to integrate neural networks into these models, and Lux.jl to construct neural network architectures. Additionally, we use Optimization.jl and OptimizationOptimisers.jl to fine-tune parameters using gradient-based methods like Adam and BFGS.
Unlike traditional ODE models that rely on fixed parameters, our UDE model replaces the key growth parameters in the equations with neural networks. This enables our UDE model to adapt better to the experimental data compared to the traditional models. This not only improves the accuracy of our predictions, but we can also effectively forecast future tumor growth with greater precision. Moreover, our approach allows for better personalization of medical treatment, as tumor growth predictions can be tailored to an individual’s clinical history.
By combining SciML techniques with traditional tumor modeling equations, our research provides a data-driven approach for optimizing treatment planning and improving clinical decision-making in oncology. This could also pave the way for more advancements in precision medicine, particularly in oncology.
Kavya is a rising junior at Boston University majoring in Mathematics and Computer Science on a full-tuition merit scholarship (Trustee Scholarship). She is an AI/ML Fellow at MIT’s Break Through Tech AI Fellowship, a researcher in the Computational Neuroscience and Vision Lab, and also serves as the Vice President of BU’s Girls Who Code chapter. Kavya is passionate about leveraging SciML to drive innovations at the intersection of medicine and technology.