Multimode fibers (MMFs) play an increasing role in optical communication, ultra-thin fiber endoscopy systems, and fiber lasers. The characterization of light propagation properties through active and passive MMFs attracts high interest as many linear optical phenomena fundamentally depend on the interplay among multiple spatial modes. Access to the exact modal amplitudes and phase weights via mode decomposition (MD) provides a useful means of investigating the physical effects. It facilitates technological advances in telecommunications, endoscopy, sensors, and amplifiers that utilize MMFs. We present an untrained neural network assisted by a linear physical model of the multimode waveguide that carries out computational MD. For the first time, the reconstructed amplitude distribution achieves a high correlation coefficient, either for thousands of modes in a short MMF or for tens of modes in a 1-km-long MMF. We also investigate the limitations of MD based on single-shot intensity images by evaluating the relative modal errors and the effect of image resolution on the decomposition accuracy. We demonstrate our network framework and results on both passive and active multimode photonic systems. Our approach holds great promise for applications in fiber lasers, endoscopic computational imaging, and especially in fiber-based communication, where fiber crosstalk is heavy and reference-free calibration techniques are required.