MediMath Science

This piece offers a personal reflection on the relevance of today’s university system—often characterized by high costs and structural inefficiencies—in the context of AI’s growing influence on how knowledge is delivered and how research is conducted. While many of these issues have already been widely discussed, the aim here is not to revisit familiar arguments. Instead, the focus is on concerns that are less frequently addressed, particularly the inefficiencies that built up in higher education between 2000 and 2020—developments that, from some perspectives, have made university education feel increasingly ineffective, or even unnecessary. To begin, it may be helpful to consider a parallel in the world of Go (baduk). Before AlphaGo, Go education followed a traditional model: aspiring players trained in academies under the close guidance of veteran instructors. These teachers shaped their students’ progress, corrected their form, and provided psychological support during losing strea...

!!!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...