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   https://doi.org/10.1364/CLEO_QELS.2022.FM2B.4  

   Ng, Edwin; Yanagimoto, Ryotatsu; Jankowski, Marc; Mabuchi, Hideo (January 2022, CLEO: QELS_Fundamental Science 2022)
2. Nonlinear Eigenvalue Methods for Linear Pointwise Stability of Nonlinear Waves

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   Scheel, Arnd (April 2023, SIAM Journal on Numerical Analysis)
3. Nonlinear multimode photonics: nonlinear optics with many degrees of freedom

   https://doi.org/10.1364/OPTICA.461981  

   Wright, Logan_G; Renninger, William_H; Christodoulides, Demetri_N; Wise, Frank_W (July 2022, Optica)

   The overall goal of photonics research is to understand and control light in new and richer ways to facilitate new and richer applications. Many major developments to this end have relied on nonlinear optical techniques, such as lasing, mode-locking, and parametric downconversion, to enable applications based on the interactions of coherent light with matter. These processes often involve nonlinear interactions between photonic and material degrees of freedom spanning multiple spatiotemporal scales. While great progress has been made with relatively simple optimizations, such as maximizing single-mode coherence or peak intensity alone, the ultimate achievement of coherent light engineering is complete, multidimensional control of light–light and light–matter interactions through tailored construction of complex optical fields and systems that exploit all of light’s degrees of freedom. This capability is now within sight, due to advances in telecommunications, computing, algorithms, and modeling. Control of highly multimode optical fields and processes also facilitates quantitative and qualitative advances in optical imaging, sensing, communication, and information processing since these applications directly depend on our ability to detect, encode, and manipulate information in as many optical degrees of freedom as possible. Today, these applications are increasingly being enhanced or enabled by both multimode engineering and nonlinearity. Here, we provide a brief overview of multimode nonlinear photonics, focusing primarily on spatiotemporal nonlinear wave propagation and, in particular, on promising future directions and routes to applications. We conclude with an overview of emerging processes and methodologies that will enable complex, coherent nonlinear photonic devices with many degrees of freedom. 

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4. Nonlinear Information Bottleneck

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   Kolchinsky, Artemy; Tracey, Brendan D.; Wolpert, David H. (December 2019, Entropy)

   Information bottleneck (IB) is a technique for extracting information in one random variable X that is relevant for predicting another random variable Y. IB works by encoding X in a compressed “bottleneck” random variable M from which Y can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete X and Y with small state spaces, and continuous X and Y with a Gaussian joint distribution (in which case optimal encoding and decoding maps are linear). We propose a method for performing IB on arbitrarily-distributed discrete and/or continuous X and Y, while allowing for nonlinear encoding and decoding maps. Our approach relies on a novel non-parametric upper bound for mutual information. We describe how to implement our method using neural networks. We then show that it achieves better performance than the recently-proposed “variational IB” method on several real-world datasets. 

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5. Nonlinear anisotropic viscoelasticity

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   Sadik, Souhayl; Yavari, Arash (January 2024, Journal of the Mechanics and Physics of Solids)