Ziyan Liu
Publications
AutoPDE: Reliable Agentic PDE Solving via Explicitly Represented Solver Strategies
Numerical solvers for partial differential equations (PDEs) are core computational tools in science and engineering. Building reliable PDE solvers requires not only executable code, but a numerical solver strategy, a set of decisions about discretization, stabilization, solver configuration, and resolution control, that matches the PDE structure. Recent LLM-based coding agents have begun to reduce the programming burden by generating and debugging solver implementations. However, they typically move directly from a PDE problem to solver code, leaving the solver strategy implicit in implementation details. Feedback from a failed solve is therefore routed back to code edits rather than to the underlying strategy, so numerical decisions remain hard to check before code is generated and hard to revise using numerical evidence when it fails. To address this limitation, we propose AutoPDE, a code agent that maintains the solver strategy as an explicitly represented object throughout the solving process: an independent, inspectable object that is built before any code is written and can be revised, using numerical evidence, whenever a solve fails. AutoPDE builds and maintains this object in three stages, all drawing from a library of reusable PDE-solving skills: PDE analysis identifies the equation type and algebraic structure; numerical method selection chooses a numerical method that matches the analysis result and commits to a discretization, stabilization, and linear solver accordingly; and adaptive tuning runs low-cost pilot solves to calibrate resolution and tolerances under the prescribed accuracy and runtime budget. We evaluate AutoPDE on the PDE Agent Bench, where experimental results show that AutoPDE achieves a pass rate of $54.5%$, improving over the strongest baseline by $14.2$ percentage points.
Meta-Cognitive Memory Policy Optimization for Long-Horizon LLM Agents
Memory-augmented LLM agents tackle complex long-horizon tasks by recursively summarizing interaction trajectories into compact memory. However, existing approaches typically train these memory policies using outcome-based reinforcement learning, failing to localize where intermediate memory quality degrades. As interactions unfold, ambiguous recursive summaries progressively discard task-relevant information and introduce semantic noise. This exacerbates belief deviation, obscuring the agent's estimate of the latent task state and ultimately derailing long-horizon reasoning. We therefore argue that memory optimization should focus not merely on trajectory-level success, but on the clarity of the belief induced by intermediate summaries. To this end, we introduce Belief Entropy, a self-supervised proxy that probes how uncertain the model remains about the latent task state given its current memory. Based on this proxy, we propose Metacognitive Memory Policy Optimization (MMPO). Instead of relying only on sparse outcome-based signals, MMPO provides fine-grained, memory-specific supervision via explicitly penalizing summaries that induce high epistemic uncertainty. Experiments show that MMPO consistently outperforms existing methods on diverse long-horizon tasks, maintaining 97.1% performance even when scaled to 1.75M-token contexts.
Evolve as a Team: Collaborative Self-Evolution for LLM-based Multi-Agent Systems
LLM-based multi-agent systems (MAS) have emerged as an effective paradigm for complex and long-horizon tasks. However, in real-world tasks, MAS often exhibit various failures during execution and such failures are difficult to eliminate during design. This motivates experience-driven MAS evolution, where a system improves based on its own execution experience. Yet such evolution is challenging because MAS experience is prolonged and intricate, interleaving multiple agents' execution chains and communication messages, which makes it difficult to identify what should be improved. To address this challenge, we propose Meta-Team, an experience-driven MAS evolution framework based on collaborative self-evolution. Meta-Team preserves the execution context of each agent and coordinates post-task communication, enabling agents to exchange distributed evidence for evolution. Building on this design, Meta-Team conducts multi-scale self-evolution, transforming execution experience into reusable improvements to agent behaviors, inter-agent coordination, and team-level organization. Across six long-horizon agent benchmarks, Meta-Team consistently outperforms single-agent systems, hand-crafted MAS, and prior MAS evolution methods; further analyses demonstrate that Meta-Team enables more reliable and scalable MAS self-evolution.