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This study introduces a computationally efficient method for inverse material characterization, utilizing Physics-Informed Neural Networks (PINNs) that operate on partial-field response measurements. This approach employs PINNs to reconstruct the entire spatial distribution of a system’s response from a subset of the measured response field and to infer the spatial distribution of unknown material properties. The primary computational effort involves a one-time simulation to generate potential responses for training the PINNs, which significantly enhances computational efficiency. Additionally, this research leverages PINNs to develop a model grounded in the fundamental physics described by differential equations and to assess aleatoric uncertainty due to noisy data. We present several examples, in both one and two dimensions, where the distribution of the elastic modulus is determined based on static partial-field displacement responses.