Kinetic theory and mathematical modeling have emerged as indispensable tools for elucidating the collective behaviour of complex systems. This discipline applies statistical mechanics to a diverse ...

Kinetic theory and mathematical modelling have emerged as pivotal tools in analysing complex systems – ranging from biological entities and social interactions to financial markets. These methods ...

Researchers use statistical physics and "toy models" to explain how neural networks avoid overfitting and stabilize learning in high-dimensional spaces.

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help ...

Artificial intelligence systems based on neural networks—such as ChatGPT, Claude, DeepSeek or Gemini—are extraordinarily ...

A dominant view in science is that there is a mathematical truth structuring the universe. It is assumed that the scientist’s job is to decipher these mathematical relations: once understood, they can ...

Complex systems such as metabolic pathways, ecosystems, the Internet, or human societies are comprised of large numbers of components that interact according to rules that change over time and that ...

Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly ...

Explore mathematical economics—a method utilizing quantitative tools and models for economic theory analysis. Learn its ...

Isolating the first spark of life on Earth is a matter of biology, geology, and chemistry—but it's also an amazing math problem. At least, that's how Varun Varanasi viewed it when he was a Yale ...

AI thrives on data but feeding it the right data is harder than it seems. As enterprises scale their AI initiatives, they face the challenge of managing diverse data pipelines, ensuring proximity to ...

Having levels of potassium that are too high or too low can be fatal. A new mathematical model sheds light on the often mysterious ways the body regulates this important electrolyte. Having levels of ...