Structural causal relationship and residual adversarial transfer network in small sample data

To address the challenge of predicting converter oxygen consumption under small-sample conditions, this article proposes a model that integrates residual adversarial transfer learning with structural causal inference. The model performs adversarial training using a TabResNet feature extractor and a domain discriminator to extract shared invariant features between data-rich source and sample-scarce target domains. Subsequently, the TabResNet extractor is frozen, and its trained parameters – comprising weights and biases of residual BasicBlocks, LayerNorm normalisation layers and linear transformation layers – extract invariant features from the target domain. These features are input into a TabPFN model based on structural causal relationships, enabling one-shot forward prediction using a limited set of target domain features. Experimental results on 4,695 source domain samples (Q195) and 638 target domain samples (Q235) demonstrate that the proposed model predicts oxygen consumption predominantly within 4400–4600 m <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> </mml:math> . Compared to baseline models, the approach achieves an RMSE of 40.09 m <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi mathvariant="normal">R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> of 0.964, facilitating enhanced process control and endpoint determination in industrial steelmaking practice.