We introduce a neural-network framework for parametrizing fundamental measure theory (FMT) applied to hard-sphere and Lennard-Jones fluids. Lutsko's extended scalar FMT expresses the excess free-energy density through two parameters, $A$ and $B$, which control the relative weight of tensor invariants in the third-order contribution ${\mathrm{\Phi }}_3$; different choices recover established functionals (Rosenfeld, White Bear, and the recent optimized values of Gül et al.). We treat $A$ and $B$ as learnable functions of the packing fraction $\eta =(\pi /6)\rho {\sigma }^3$, predicted by a small neural network and optimized end to end through a JAX-based density functional solver. Four training strategies are examined, namely matching the Carnahan-Starling equation of state, minimizing chemical-potential and compressibility deviations, optimizing wall contact densities, and a combined multiobjective loss. All four converge to parameters near the Percus-Yevick line defined by the constraint combination $C=8A+2B-9\approx 0$, with subpercent agreement with Carnahan-Starling thermodynamics. Extension to Lennard-Jones fluids via Weeks-Chandler-Andersen perturbation theory, using the temperature-dependent Barker-Henderson effective diameter to define an effective packing fraction, yields vapor-liquid coexistence with a critical temperature $T_c^{*}=k_B{T}_c/\epsilon \approx 1.28$, consistent with mean-field DFT benchmarks. The learned parameters remain close to the fixed Lutsko baseline ($A=1, B=0$) throughout, confirming that bulk phase equilibria alone cannot drive nontrivial density dependence. A three-phase training strategy—bulk equation-of-state fitting, test-particle sum-rule optimization, and wall-contact density fine tuning via numerical gradients—breaks this degeneracy, yielding contact densities within 1–2% of molecular dynamics data across all benchmark packing fractions and a 5.5-fold reduction in final wall-contact loss relative to direct wall fine tuning, at the cost of 5–8% bulk thermodynamic errors that quantify a genuine bulk-interface tradeoff. These results provide a starting point for adaptive density functionals trained on inhomogeneous simulation data.

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• Classical statistical mechanics
• Equations of state
• Phase diagrams