Traditional Topology Optimization (TO) is often hindered by the high computational cost of iterative FEA solvers and a lack of transferability, where a new optimization is required for every change in problem specification. This research proposes a Generalizable Neural Topology Optimization framework that shifts the paradigm from instance-based solvers to a unified neural representation. We utilize a coordinate-based neural network to represent the material distribution as a continuous field, enabling high-resolution designs with a fraction of the memory overhead. To bypass the bottleneck of traditional solvers, we integrate the Deep Energy Method (DEM) [1] for structural and thermal analysis. By minimizing the variational energy functional directly within the neural network’s loss function, the framework enforces physical consistency without requiring an external mesh-based solver. This approach is demonstrated on two foundational engineering benchmarks: steady-state heat conduction and the elastic MBB beam. In both cases, the network successfully synthesizes optimal topologies that minimize thermal compliance and maximize structural stiffness, respectively. The core contribution of this work lies in the investigation of generalizability. By training on a distribution of "distributed inputs," the model demonstrates the ability to generalize across varying loading conditions and boundary conditions in a zero-shot manner. Unlike standard TO, which must restart upon the slight shift of a load, our neural operator predicts near-optimal topologies instantaneously. This study proves that embedding variational physics into neural architectures allows for a robust design engine capable of scaling to diverse engineering environments, laying the groundwork for real-time, autonomous physical synthesis.