In variable-step operator learning, agreement at observed step sizes does not by itself determine predictions at other temporal resolutions. We propose an operator whose step-size dependence is prescribed by a first-order Duhamel approximation of semilinear dynamics. It combines exact linear propagation with a local nonlinear function of the field and its derivatives, allowing evaluation below the observation interval without supervision densely sampled across step sizes. Under suitable conditions and at fixed spatial resolution, we prove that agreement between models at two step sizes controls their prediction differences throughout a prescribed range. We also give conditions for local identifiability of both components from two step sizes, supporting interpretation of the learned structure. A latent extension applies the same construction to learned fields. We evaluate the base model on two synthetic problems and the extension on two real datasets against several baselines.
Agent-based models (ABMs) are widely used in economics and social sciences. They represent heterogeneous personal behaviors and their interactions by using simulations, whereas their likelihoods are often intractable for parameter estimations. Therefore, most traditional statistical inference techniques are hindered. Driven by recent advances in probabilistic machine learning, recent works have applied neural networks to achieve likelihood-free inference in large-scale ABMs. Specifically, Neural Posterior Estimation using normalizing flows provide amortized Bayesian inference from simulations, yet a pre-trained estimator may become inaccurate when the target task changes. In this work, we investigate the practicality of adapting a pre-trained conditional normalizing flow through a unified sequential neural posterior estimation test-time training (SNPE-TTT) framework. The framework includes four adaptation strategies: full-parameter adaptation, low-rank adaptation, and two update spaces identified from target-task gradients. We evaluate all four methods across economic simulation models with both tractable and intractable likelihoods. These benchmarks demonstrate that the sequential neural posterior estimation test-time training framework can adapt pre-trained posterior estimators to related inference tasks using a limited budget of target simulations. Posterior recovery and computational benefits depend on the task and adaptation strategy, with lower target-stage cost in some settings but no consistently superior posterior accuracy.
Neural posterior estimation (NPE) enables Bayesian inference of the posterior parameter in agent-based models (ABMs) with intractable likelihoods, but simulating training data can be computationally expensive. We propose Double-Flow Neural Posterior Estimation (DF-NPE), which combines learned time-series summaries with two conditional normalizing flows for synthetic-data generation and posterior estimation. The framework supplements direct simulations with synthetic training pairs and supports both pooled and ordered training strategies. Experiments in two settings of the Brock-Hommes asset-pricing model show that DF-NPE can reduce direct simulations by 90 percent while achieving lower mean posterior discrepancies and runtime than standard NPE. Performance varies with the allocation of directly simulated and synthetic data and the training strategy. These results establish learned summary augmentation as a practical approach to reducing simulation costs for Bayesian posterior inference of parameters in ABMs.