Neural Jump ODEs model the conditional expectation between observations by neural ODEs and jump at arrival of new observations. They have demonstrated effectiveness for fully data-driven online forecasting in settings with irregular and partial observations, operating under weak regularity assumptions. This work extends the framework to input-output systems, enabling direct applications in online filtering and classification. We establish theoretical convergence guarantees for this approach, providing a robust solution to $L^2$-optimal filtering. Empirical experiments highlight the model's superior performance over classical parametric methods, particularly in scenarios with complex underlying distributions. These results emphasise the approach's potential in time-sensitive domains such as finance and health monitoring, where real-time accuracy is crucial.

翻译：神经跳跃常微分方程通过神经常微分方程对观测值之间的条件期望进行建模，并在新观测到达时发生跳跃。该模型已在观测不规则且不完全、仅需弱正则性假设的场景中，展现出全数据驱动在线预测的有效性。本研究将该框架扩展至输入-输出系统，使其能够直接应用于在线滤波与分类任务。我们为此方法建立了理论收敛性保证，为 $L^2$ 最优滤波提供了鲁棒解决方案。实证实验表明，该模型性能优于经典参数化方法，尤其在底层分布复杂的场景中表现突出。这些结果凸显了该方法在金融与健康监测等对实时准确性要求极高的时效敏感领域的应用潜力。