arXiv:2610.35521v1 Announce Type: new Abstract: Differentially private synthesis of in-car energy consumption data is challenging because the output is high-dimensional, and known lower bounds show that the privacy-utility trade-off degrades with the square root of the number of output dimensions. However, we observe that the intrinsic dimensionality of in-car energy consumption is much lower than that of the raw trace: given a small set of contextual personal variables-such as start point, end point, the car model, and the driving behavior-the consumption profile can be largely explained by publicly available map data (including elevation) combined with a physical model of vehicle energy use. We exploit this low intrinsic dimensionality in PRISMA, a Privacy-preserving In-car Synthesis and Modelling Algorithm. PRISMA involves three stages: (i) energy consumption traces are encoded into a low-dimensional latent space; (ii) the distribution of latent vectors is synthesized using the differentially private tabular data synthesis algorithm AIM, and (iii) samples drawn from this distribution are decoded back into full energy consumption traces via a differentiable physics-based simulation, a step that consumes no additional privacy budget since it uses only public information. By using a compact, physically-grounded latent representation of the traces, PRISMA significantly reduces the effective output dimension. Our experimental results show that PRISMA achieves for a competitive $\varepsilon = 0.5$ a better data synthesis performance than prior tabular and marginal-based DP synthesis baselines by preserving the diversity of the original power consumption profiles without collapsing to a small set of modes.