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Abstract Physics-Informed Neural Networks (PINNs) have opened new possibilities for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. However, despite their flexibility, traditional PINNs often struggle to capture sharp gradients and intricate solution features, which limits their effectiveness in many practical problems. In this work, we have introduced Gradient-Driven Physics-Informed Neural Networks (GDPINNs) that improve the ability of traditional PINNs to resolve sharp gradients. By incorporating gradient information directly into the loss function, GDPINNs better target regions where traditional PINNs typically fail. We validated the method on steady-state and transient heat conduction problems, including a central heating source and a sinusoidal boundary condition, and found strong agreement with reference solutions. To further understand the framework's capability, we applied it to a high-gradient steady-state and transient heat conduction problem, where GDPINNs show clear advantages over traditional PINNs and align closely with reference results. We also extended GDPINNs to incompressible laminar flow in a lid-driven cavity, demonstrating its broader applicability. In these cases, GDPINNs consistently provide higher accuracy and better capture critical solution features, highlighting their potential to improve PINNs-based approaches for complex physical problems with sharp gradients. 

Potassium-ion batteries (KIBs) are a promising alternative to lithium-ion batteries (LIBs) due to the abundance and low cost of the raw materials needed for their production, with target applications including grid-scale renewable energy storage. However, their performance, particularly cycling stability, remains an issue. In this study, we explore the use of the cyclic ethers tetrahydropyran (THP) and tetrahydrofuran (THF) as alternative solvents to the traditional ethylene carbonate/propylene carbonate (EC/PC) system in potassium metal batteries (KMBs). By changing the electrolyte solvent to create more anion-rich solvation structures, the formation of a thinner, more robust cathode-electrolyte interface (CEI) on high-potential Prussian blue analogue (PBA) cathodes is achieved. This results in improved capacity retention (97% for THP, 87% for THF, vs 78% for EC/PC) and higher Coulombic efficiency (94.0% for THP, 96.6% for THF, vs 66.2% for EC/PC) in K metal||PBA cells. Additionally, we find that THF in particular incurs these benefits both with high potential (∼4.3 V vs K/K⁺) PBA cathodes as well as lower potential (∼3.5 V vs K/K⁺) organic cathode materials. These findings can help further the design of electrolytes to realize KIBs and KMBs as a sustainable and viable alternative to lithium-based systems for applications at scale. 

Retrieval-Augmented Generation (RAG) has significantly mitigated the hallucinations of Large Language Models (LLMs) by grounding the generation with external knowledge. Recent extensions of RAG to graph-based retrieval offer a promising direction, leveraging the structural knowledge for multi-hop reasoning. However, existing graph RAG typically decouples retrieval and reasoning processes, which prevents the retriever from adapting to the reasoning needs of the LLM. They also struggle with scalability when performing multi-hop expansion over large-scale graphs, or depend heavily on annotated ground-truth entities, which are often unavailable in opendomain settings. To address these challenges, we propose a novel graph retriever trained endto-end with LLM, which features an attentionbased growing and pruning mechanism, adaptively navigating multi-hop relevant entities while filtering out noise. Within the extracted subgraph, structural knowledge and semantic features are encoded via soft tokens and the verbalized graph, respectively, which are infused into the LLM together, thereby enhancing its reasoning capability and facilitating interactive joint training of the graph retriever and the LLM reasoner. Experimental results across three QA benchmarks show that our approach consistently achieves state-of-the-art performance, validating the strength of joint graph–LLM optimization for complex reasoning tasks. Notably, our framework eliminates the need for predefined ground-truth entities by directly optimizing the retriever using LLM logits as implicit feedback, making it especially effective in open-domain settings.