MediMath Science

This piece offers a personal reflection on the relevance of today’s university system in a world where AI increasingly shapes how knowledge is delivered and how research is conducted. Rather than revisiting familiar debates, the focus here is on less-discussed inefficiencies that have gradually taken root within higher education. A helpful parallel can be found in the world of Go (baduk). Before AlphaGo, Go education relied on apprenticeship: students trained under veteran instructors who refined their technique and supported them through setbacks. This changed dramatically after AlphaGo’s 2016 victory over Lee Sedol. AI tools such as KataGo and Leela Zero now guide much of young players’ learning, offering strategies that challenge and often surpass long-held conventions. One Korean prodigy reportedly trained almost exclusively with AI for a year, developing an unconventional style that quickly carried him to the top. Human mentors still matter, but their role has shifted toward inter...

!!!Needs revision!!! Physics-Informed Neural Networks (PINNs) aim to approximate the solution \( u \) of a differential equation defined over spatial coordinates \( x \in \mathbb{R}^d \) (e.g., \( x = (x_1, x_2, x_3) \)), and, when applicable,  time \( t \), by representing \( u \) with a neural network \( u_\theta \), where \( \theta \) denotes the trainable weights and biases. Training involves minimizing a composite loss function  $\mathcal{L}(\theta) = \mathcal{L}_{\text{PDE}} + \mathcal{L}_{\text{BC}} + \mathcal{L}_{\text{IC}} + \mathcal{L}_{\text{data}},$ which enforces the governing PDE, boundary conditions, initial conditions, and any available observational data.   However, PINNs minimize the PDE residual only indirectly—by adjusting the neural network parameters rather than manipulating solution components or their derivatives in a controlled, explicit manner. This leads to several fundamental inefficiencies. Since the solution is represented by a neural n...