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This paper presents an adjustment-based modeling framework for statistical static timing analysis (SSTA) when the dimension of parameter variability is high. Instead of building a complex model between the circuit timing and parameter variability, we build a model which adjusts an approximate variation-aware timing into an accurate one. The intuition is that it is simpler to build a model which adjusts an approximate estimate into an accurate one. It is also more efficient to obtain an approximate circuit timing model. The combination of these two observations makes the use of an adjustment-based model a good choice for SSTA with high dimension of parameter variability. To build the adjustment model, we use a simulation-based approach, which is based on Gaussian Process. Combined with intelligent sampling, we show that an adjustment-based model can more effectively capture the nonlinearity of the circuit timing with respect to parameter variability compared to polynomial modeling. We also show that with only 200 samples of the circuit timing and 42 independent parameter variations, adjustment-based modeling obtains higher accuracy than direct SSTA using quadratic modeling.