Since the earliest stages of human civilization, advances in technology have been tightly linked to our ability to understand and predict the mechanical behavior of materials. In recent years, this challenge has increasingly been framed within the broader paradigm of data-driven scientific discovery, where governing laws are inferred directly from observations. However, existing methods require either stress-strain pairs or full-field displacement measurements, which are often inaccessible in practice. We introduce Neural-DFEM, a method that enables unsupervised discovery of hyperelastic material laws even from partial observations, such as boundary-only measurements. The method embeds a differentiable finite element solver within the learning loop, directly linking candidate energy functionals to available measurements. To guarantee thermodynamic consistency and mathematical well-posedness throughout training, the method employs Hyperelastic Neural Networks, a novel structure-preserving neural architecture that enforces frame indifference, material symmetry, polyconvexity, and coercivity by design. The resulting framework enables robust material model discovery in both two- and three-dimensional settings, including scenarios with boundary-only measurements. Neural-DFEM allows for generalization across geometries and loading conditions, and exhibits unprecedented accuracy and strong resilience to measurement noise. Our results demonstrate that reliable identification of material laws is achievable even under partial observability when strong physical inductive biases are embedded in the learning architecture.

翻译：自人类文明早期阶段，技术进步一直与我们理解和预测材料力学行为的能力紧密相连。近年来，这一挑战日益被纳入数据驱动科学发现的更广泛范式，即从观测中直接推断支配定律。然而，现有方法要么需要应力-应变配对数据，要么需要全场位移测量，而这些在实际中通常难以获取。我们提出Neural-DFEM方法，该方法即使仅从部分观测（如仅边界测量）也能实现超弹性材料定律的无监督发现。该方法将可微有限元求解器嵌入学习循环中，直接将候选能量泛函与可用测量数据相关联。为确保训练过程中的热力学一致性和数学适定性，该方法采用超弹性神经网络——一种新颖的结构保持神经架构，通过设计强制满足框架无关性、材料对称性、多凸性和强制条件。由此形成的框架可在二维和三维场景中实现稳健的材料模型发现，包括仅边界测量的情况。Neural-DFEM支持跨几何形状和加载条件的泛化，并展现出前所未有的精度和对测量噪声的强鲁棒性。我们的结果表明，当学习架构中嵌入强物理归纳偏置时，即使在部分可观测条件下也能实现材料定律的可靠识别。