A central aspect of the SPIN framework is nonlinearity. Many scientific and engineering systems are inherently nonlinear, yet theoretical tools for nonlinear systems remain far less developed than those for linear systems.
For decades, engineering disciplines such as communications, signal processing, and control theory have benefited from powerful mathematical frameworks for analyzing and designing linear systems. However, many real-world phenomena—including physical processes, complex networks, and high-dimensional data systems—are fundamentally nonlinear.
Deep neural networks have emerged as general-purpose nonlinear modeling tools, capable of approximating complex functional relationships directly from data. Their success highlights the importance of developing more systematic approaches to nonlinear modeling, learning, and prediction.
This perspective motivates the development of engineering AI, where modern learning systems are applied to challenging nonlinear problems arising in scientific and engineering domains.
Examples include:
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nonlinear system identification
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high-dimensional function approximation
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predictive modeling of complex physical processes.
Our research explores new approaches for improving the nonlinear modeling capability of learning systems, including the design of more expressive nonlinear operators and architectures. For example, recent work has investigated new families of trainable activation functions capable of approximating complex nonlinear functions with high precision.
A deeper goal of this direction is to develop neural architectures with rigorous theoretical foundations for nonlinear function approximation — moving from the existential guarantees of classical approximation theory toward constructive principles that specify both architecture and the design of nonlinear operators. Applications include solving partial differential equations and approximating high-dimensional nonlinear functions arising in science and engineering.