The characterization of fission-driven nuclear systems primarily relies on calculations of neutron-induced chain reactions, and these calculations require evaluated nuclear data as input. Calculation accuracy heavily depends on input nuclear data evaluation accuracy, and thus high precision on the experimental input to the nuclear data evaluation is essential for fundamental quantities like the energy spectrum of neutrons emitted from neutron-induced fission (i.e., the prompt fission neutron spectrum, PFNS). Despite decades of measurement efforts, prior to the measurements described in this work there were only three literature data sets for the $^{235}\mathrm{U}(n,f)$ PFNS at incident neutron energies above 1.0 MeV considered reliable for inclusion in nuclear data evaluations and no reliable data sets above 3.0 MeV incident neutron energy. In this work we report on new measurements of the $^{235}\mathrm{U}(n,f)$ PFNS spanning a grid of 1.0--20.0 MeV in incident neutron energy and 0.01--10.0 MeV in outgoing (PFNS) neutron energy. These measurements were carried out at the Weapons Neutron Research facility at the Los Alamos Neutron Science Center and used a multifoil parallel-plate avalanche counter target with both a Li-glass and a liquid scintillator detector array in separate experiments to span the quoted outgoing neutron energy ranges. The PFNS results are shown in terms of the energy spectra themselves as well as the average PFNS energy ($\ensuremath{\langle}E\ensuremath{\rangle}$) and ratios of $\ensuremath{\langle}E\ensuremath{\rangle}$ at forward and backward angles. The results are compared with literature data and selected nuclear data evaluations. Generally, the data agree with the ENDF/B-VIII.0 evaluation below 5.0-MeV incident neutron energy and more closely with the JEFF-3.3 evaluation above 5.0 MeV, though no evaluations considered for comparison in this work agree with the data across all of the incident and outgoing neutron energies shown, especially in regions where the third-chance fission process becomes available. Additionally, we show a ratio of the present PFNS results for $^{235}\mathrm{U}(n,f)$ with a recent and highly correlated experiment to measure the $^{239}\mathrm{Pu}(n,f)$ PFNS at the same experimental facility and with nearly identical equipment and analysis procedures. Many observations reported in this work are the first of their kind and represent significant advancements for knowledge of the $^{235}\mathrm{U}(n,f)$ PFNS.
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