宾夕法尼亚大学的研究人员开发了一种更智能的人工智能方法，用于求解极难处理的逆方程，这类方程有助于科学家揭示可观测现象背后的隐藏成因。通过引入能够平滑噪声数据的“磨光层”，他们使这些计算变得更加稳定，且计算需求大幅降低。这一成果有望变革遗传学等领域，因为在这些领域中，理解DNA的行为方式是疾病研究的关键。
"Solving an inverse problem is like looking at ripples in a pond and working backward to figure out where the pebble fell," says Vivek Shenoy, Eduardo D. Glandt President's Distinguished Professor in Materials Science and Engineering (MSE) and senior author of a study published in Transactions on Machine Learning Research (TMLR), which will be presented at the Conference on Neural Information Processing Systems (NeurIPS 2026). "You can see the effects clearly, but the real challenge is inferring the hidden cause."
` * *Draft:* “解决反问题就像看着池塘里的涟漪并倒推找出鹅卵石落在哪里，”Vivek Shenoy说，他是材料科学与工程（MSE）的Eduardo D. Glandt校长特聘教授，也是发表在《机器学习研究汇刊》（TMLR）上的一项研究的资深作者，该研究将在神经信息处理系统会议（NeurIPS 2026）上展示。“你可以清楚地看到效果，但真正的挑战是推断隐藏的原因。” * *Refinement:* * "Inverse problem" -> 反问题. * "Eduardo D. Glandt President's Distinguished Professor" -> Eduardo D. Glandt 校长特聘教授. * "Senior author" -> 资深作者 / 通讯作者. In academic papers, "senior author" usually corresponds to the PI, often translated as 资深作者 or 通讯作者. Let's use 资深作者 to be literal yet accurate. * "Transactions on Machine Learning Research" -> 《机器学习研究汇刊》. * "Conference on Neural Information Processing Systems" -> 神经信息处理系统大会. * *Polishing:* “解决反问题就像观察池塘中的涟漪，并反向推导石子落入的位置，”材料科学与工程（MSE）系Eduardo D. Glandt校长特聘教授、发表于《机器学习研究汇刊》（*TMLR*）的一项研究的资深作者Vivek Shenoy说道，该研究将在神经信息处理系统大会（NeurIPS 2026）上展示。“你可以清楚地看到结果，但真正的挑战在于推断其背后的隐因。” * **Segment 3:** * *Source:* `Instead of relying on more powerful hardware, the researchers focused on improving the underlying mathematics. "Modern AI often advances by scaling up computation," says Vinayak Vinayak, a doctoral candidate in MSE and co-first author of the study. "But some scientific challenges require better mathematics, not just more compute."
` * *Draft:* 研究人员没有依赖更强大的硬件，而是专注于改进底层数学。“现代AI通常通过扩大计算规模来进步，”Vinayak Vinayak说，他是MSE的博士候选人兼该研究的共同第一作者。“但一些科学挑战需要更好的数学，而不仅仅是更多的计算。” * *Refinement:* * "Scaling up computation" -> 扩大计算规模 / 增加算力规模. * "Co-first author" -> 共同第一作者. * "More compute" -> 更多算力 / 更多计算资源. * *Polishing:* 研究人员并未依赖更强大的硬件，而是专注于改进底层数学。“现代AI的进步往往依赖于扩大计算规模，”MSE系博士候选人、该研究共同第一作者Vinayak Vinayak说道，“但某些科学挑战需要更优的数学方法，而不仅仅是更多的算力。” * **Segment 4:** * *Source:* `Why Inverse PDEs Matter in Science
` * *Draft:* 为什么反偏微分方程在科学中很重要 * *Refinement:* PDE = Partial Differential Equation = 偏微分方程. * *Polishing:* **反偏微分方程在科学中的重要性** * **Segment 5:** * *Source:* `Differential equations are the backbone of scientific modeling. They describe how systems change over time, whether it is population growth, heat flow, or chemical reactions.
` * *Draft:* 微分方程是科学建模的支柱。它们描述系统如何随时间变化，无论是人口增长、热流还是化学反应。 * *Polishing:* 微分方程是科学建模的基石。无论是人口增长、热流传递还是化学反应，它们都能描述系统随时间的演变过程。 * **Segment 6:** * *Source:* `Partial differential equations extend this idea further by capturing how systems evolve across both space and time. Scientists use them to study everything from weather patterns to how heat moves through materials and even how DNA is organized inside cells.
` * *Draft:* 偏微分方程通过捕捉系统如何在空间和时间上演变，进一步扩展了这一思想。科学家使用它们来研究从天气模式到热量如何在材料中移动，甚至DNA如何在细胞内组织的所有事情。 * *Refinement:* "Capturing" -> 捕捉 / 描述. "Organized" -> 组织 / 排列. * *Polishing:* 偏微分方程通过捕捉系统在空间和时间维度上的演化，进一步拓展了这一概念。科学家利用它们研究各类现象，从天气模式到热量在材料中的传导，甚至细胞内DNA的组织方式。 * **Segment 7:** * *Source:* `Inverse PDEs go a step further. Rather than predicting outcomes based on known rules, they allow scientists to start with observed data and work backward to uncover the hidden forces driving those observations.
` * *Draft:* 反偏微分方程更进一步。它们不是根据已知规则预测结果，而是允许科学家从观察到的数据开始，反向推导以揭示驱动这些观察结果的隐藏力量。 * *Refinement:* "Inverse PDEs" -> 反偏微分方程问题 (usually refers to solving inverse problems involving PDEs). The text says "Inverse PDEs", I will translate as "反偏微分方程". * *Polishing:* 反偏微分方程则更进一步。它们并非基于已知规则预测结果，而是允许科学家从观测数据出发，通过反向推导揭示驱动这些观测结果的潜在力量。 * **Segment 9:** * *Source:* `"For years, we've used these equations to study how chromatin, which is the folded state of DNA inside the nucleus, organizes itself inside living cells," says Shenoy. "But we kept running into the same problem: We could see the structures and model their formation, but we could not reliably infer the epigenetic processes driving this system, namely the chemical changes that help control which genes are active. The more we tried to optimize the existing approach, the clearer it became that the mathematics itself needed to change."
` * *Draft:* “多年来，我们一直使用这些方程来研究染色质（即细胞核内DNA的折叠状态）如何在活细胞内组织自己，”Shenoy说。“但我们一直遇到同样的问题：我们可以看到结构并模拟它们的形成，但我们无法可靠地推断驱动该系统的表观遗传过程，即帮助控制哪些基因活跃的化学变化。我们越是试图优化现有方法，就越清楚地认识到数学本身需要改变。” * *Refinement:* * "Chromatin" -> 染色质. * "Epigenetic processes * Draft: 传统上，AI系统使用一种称为递归自动微分的过程来计算这些导数。该方法在数据通过神经网络（现代AI的基础）时反复计算变化。 * Refinement: "Recursive automatic differentiation" -> 递归自动微分. "Neural network" -> 神经网络. The flow is good. * *Para 2:* "However, this approach struggles when dealing with complex systems and noisy data. It can become unstable and demand enormous computing resources." * Draft: 然而，这种方法在处理复杂系统和噪声数据时很吃力。它可能变得不稳定，并需要巨大的计算资源。 * Refinement: "Struggles" -> 表现不佳 / 难以应对. "Noisy data" -> 噪声数据. "Enormous" -> 巨大的 / 海量的. Let's use "难以应对" for struggles. * *Para 3:* "The researchers compare it to repeatedly zooming in on a rough, jagged line. Each step amplifies imperfections, making the final result less reliable. To overcome this, the team realized they needed a way to smooth the data before analyzing it." * Draft: 研究人员将其比作反复放大一条粗糙、锯齿状的线条。每一步都会放大缺陷，使最终结果不太可靠。为了克服这一点，团队意识到他们需要在分析数据之前对其进行平滑处理。 * Refinement: "Rough, jagged line" -> 粗糙、参差不齐的线条. "Imperfections" -> 缺陷 / 不完美之处. "Smooth" -> 平滑. * *Heading 1:* "Mollifier Layers Offer a Smarter Solution" * Draft: “磨光层”提供了更智能的解决方案。 * Refinement: "Mollifier" is a specific mathematical term. In Chinese math contexts, it is often translated as "磨光函数" or "软化子", but here it's a "layer". "磨光层" or "平滑层" works. Given the context of smoothing, "磨光层" is technically accurate for "mollifier". Let's stick to "磨光层" or "平滑算子层". Let's check standard translations. Mollifier -> 磨光算子 / 磨光函数. So "Mollifier Layer" -> 磨光层. * *Para 5:* "The answer came from a concept introduced in the 1940s by mathematician Kurt Otto Friedrichs, who described 'mollifiers,' tools designed to smooth irregular or noisy functions." * Draft: 答案来自数学家Kurt Otto Friedrichs在1940年代引入的一个概念，他描述了“磨光子”，即设计用于平滑不规则或噪声函数的工具。 * Refinement: "Mollifiers" -> 磨光算子 / 磨光子. "Functions" -> 函数. * *Para 6:* "By adapting this idea, the researchers created a 'mollifier layer' within AI models. This layer smooths the input data before calculating changes, avoiding the instability caused by traditional methods." * Draft: 通过改编这一想法，研究人员在AI模型中创建了一个“磨光层”。该层在计算变化之前平滑输入数据，避免了传统方法导致的不稳定性。 * Refinement: "Adapting" -> 改进 / 借鉴. "Calculating changes" -> 计算变化 (referring to derivatives). * *Para 7:* "'We initially assumed the issue had to do with neural network's architecture,' says Ananyae Kumar Bhartari, a graduate of Penn Engineering's Scientific Computing master's program and the paper's other co-first author. 'But, after carefully adjusting the network, we eventually realized the bottleneck was recursive automatic differentiation itself.'" * Draft: “我们最初假设问题与神经网络的架构有关，”宾夕法尼亚大学工程学院科学计算硕士项目的毕业生、该论文的另一位共同第一作者Ananyae Kumar Bhartari说。“但是，在仔细调整网络后，我们最终意识到瓶颈在于递归自动微分本身。” * Refinement: "Penn Engineering" -> 宾夕法尼亚大学工程学院. "Co-first author" -> 共同第一作者. "Bottleneck" -> 瓶颈. * *Para 8:* "The results were striking. The new method reduced noise and significantly lowered the computational cost required to solve these equations." * Draft: 结果令人瞩目。新方法减少了噪声，并显著降低了解决这些方程所需的计算成本。 * Refinement: "Striking" -> 惊人 / 令人瞩目. "Computational cost" -> 计算成本. * *Para 9:* "Implementing a 'mollifier layer,' which smoothed the signal before measuring it, radically diminished both the noisiness and the power consumption scaling. 'That let us solve these equations more reliably, without the same computational burden,' says Bhartari." * Draft: 实施“磨光层”在测量信号之前对其进行平滑，从根本上减少了噪声和功耗扩展。“这让我们能够更可靠地求解这些方程，而没有同样的计算负担，”Bhartari说。 * Refinement: "Power consumption scaling" -> 功耗扩展 / 功耗规模增长. "Scaling" usually refers to how resource usage grows. "Radically diminished" -> 根本上减少 / 大幅降低. Let's use "大幅降低了噪声和功耗的增长规模". Or simply "功耗". "Scaling" implies the rate at which power consumption increases. Let's translate as "功耗规模". Actually, "power consumption scaling" often refers to how power usage scales with problem size. Let's say "功耗增长". Let's stick to "功耗规模" or just "功耗" if the nuance is too subtle, but "scaling" is specific. Let's use "功耗扩展性" or "功耗规模". Let's go with "大幅降低了噪声和功耗规模". * *Heading 2:* "Unlocking the Secrets of DNA Organization" * Draft: 揭示DNA组织的奥秘 * Refinement: "Organization" -> 组织 / 组装. In chromatin context, "organization" is usually "组织" or "空间结构". "DNA组织" is fine. * *Para 11:* "One of the most promising applications of this approach lies in understanding chromatin, the complex structure of DNA and proteins inside cells." * Draft: 该方法最有前途的应用之一在于理解染色质，即细胞内DNA和蛋白质的复杂结构。 * Refinement: "Chromatin" -> 染色质. "Promising" -> 有前景 / 有前途. * *Para 12:* "These structures operate at an incredibly small scale, but they play a major role in determining how genes are turned on or off." * Draft: 这些结构在极小的尺度上运作，但它们在决定基因如何开启或关闭 * *Wide-Ranging Scientific Impact:* 广泛的科学影响 / 深远的科学影响. "广泛的科学影响" is accurate. * *Draft:* 超越生物学：广泛的科学影响 * **Paragraph 1:** `The potential uses of mollifier layers extend far beyond genetics. Many areas of science, including materials research and fluid dynamics, involve complex equations and noisy data.
` * *mollifier layers:* This is a specific mathematical/technical term. "Mollifier" usually translates to "磨光函数" or "软化子" in mathematics. "Mollifier layers" would be "磨光层" or "软化层". Given the context of neural networks or computational layers (implied by "layers"), "磨光层" is a standard mathematical translation for the concept of smoothing/regularizing. Let's stick with "磨光层" (or potentially "平滑层" if the context suggests a specific neural network architecture, but "磨光" is the precise math term). Let's use "磨光层". * *extend far beyond genetics:* 远不止于遗传学 / 远超遗传学. * *materials research:* 材料研究. * *fluid dynamics:* 流体动力学. * *complex equations:* 复杂方程. * *noisy data:* 噪声数据. * *Draft:* 磨光层的潜在用途远不止于遗传学。许多科学领域，包括材料研究和流体动力学，都涉及复杂的方程和噪声数据。 * **Paragraph 2:** `This new framework could provide a more stable and efficient way to uncover hidden parameters across a wide variety of systems.
` * *framework:* 框架. * *stable and efficient:* 稳定且高效. * *uncover hidden parameters:* 揭示隐藏参数 / 发掘隐含参数. * *across a wide variety of systems:* 在各种系统中 / 跨越多种系统. * *Draft:* 这一新框架可以为揭示多种系统中的隐藏参数提供一种更稳定、更高效的方法。 * **Paragraph 3:** `The researchers see this as a step toward a larger goal: turning observations into deeper understanding.
` * *The researchers see this as...:* 研究人员将此视为... * *step toward a larger goal:* 迈向更大目标的一步. * *turning observations into deeper understanding:* 将观察转化为更深层次的理解. * *Draft:* 研究人员将此视为迈向更大目标的一步：将观察转化为更深层次的理解。 * **Paragraph 4:** `"Ultimately, the goal is to move from observing complex patterns to quantitatively uncovering the rules that generate them," says Shenoy. "If you understand the rules that govern a system, you now have the possibility of changing it."
` * *Ultimately:* 归根结底 / 最终. * *move from observing complex patterns to...:* 从观察复杂模式转变为... * *quantitatively uncovering the rules:* 定量揭示...的规律/规则. * *generate them:* 生成它们. * *Shenoy:* 申诺伊 (transliteration, usually keep the name or transliterate standardly). Let's use "Shenoy" or "Shenoy（申诺伊）". Since the prompt asks for professional translation, transliterating names is standard unless the English name is preferred in specific journals. I will translate the quote and attribute it to Shenoy. * *govern a system:* 支配系统 / 统治系统. "支配" is good for physics/systems. * *possibility of changing it:* 改变它的可能性. * *Draft:* “归根结底，目标是从观察复杂模式转变为定量揭示生成这些模式的规律，”Shenoy说。“如果你理解了支配一个系统的规律，你就拥有了改变它的可能性。” * **Paragraph 5 (Funding):** `This study was conducted at the University of Pennsylvania School of Engineering and Applied Science and supported by National Cancer Institute (NCI) Award U54CA261694 (V.B.S.); National Science Foundation (NSF) Center for Engineering Mechanobiology (CEMB) Grant CMMI -154857 (V.B.S.); NSF Grant DMS -2347834 (V.B.S.); National Institute of Biomedical Imaging and Bioengineering (NIBIB) Awards R01EB017753 (V.B.S) and R01EB030876 (V.B.S.) and National Institute of General Medical Sciences (NIGMS) Award R01GM155943 (V.B.S.).
` * *University of Pennsylvania School of Engineering and Applied Science:* 宾夕法尼亚大学工程与应用科学学院. * *National Cancer Institute (NCI):* 美国国家癌症研究所 (NCI). * *Award U54CA261694:* 奖项 U54CA261694. * *National Science Foundation (NSF):* 美国国家科学基金会 (NSF). * *Center for Engineering Mechanobiology (CEMB):* 工程力生物学中心 (CEMB). * *Grant CMMI -154857:* 拨款 CMMI -154857. 注明: The source text has a space before the hyphen. I should preserve the grant number format exactly as it appears or standardly formatted. Usually, grant numbers are kept as is. * *National Institute of Biomedical Imaging and Bioengineering (NIBIB):* 美国国立生物医学影像与生物工程研究所 (NIBIB). * *National Institute of General Medical Sciences (NIGMS):* 美国国立综合医学科学研究所 (NIGMS). * *(V.B.S.):* These are likely principal investigator initials (Vivek B. Shenoy). I should keep them as (V.B.S.). * *Draft:* 本研究在宾夕法尼亚大学工程与应用科学学院进行，并获得了美国国家癌症研究所 (NCI) 奖项 U54CA261694 (V.B.S.)；美国国家科学基金会 (NSF) 工程力生物学中心 (CEMB) 拨款 CMMI -154857 (V.B.S.)；NSF 拨款 DMS -2347834 (V.B.S.)；美国国立生物医学影像与生物工程研究所 (NIBIB) 奖项 R01EB017753 (V.B.S) 和 R01EB030876 (V.B.S.)；以及美国国立综合医学科学研究所 (NIGMS) 奖项 R01GM155943 (V.B.S.) 的支持。 3. **Review and Refine:** * *Term check:* "Mollifier layers" -> "磨光层". This is the standard mathematical term for mollifiers used in analysis and PDEs. In the context of machine learning/physics-informed neural networks, this fits. * *Flow check:* The Chinese flows well. The funding section is dense but accurate. * *Formatting:* Keep the HTML tags ``, ``, `` as implied by the source structure, or just output the text? The prompt asks to translate the content. Usually, if the input has HTML tags, the output should ideally reflect the structure, but often users just want the text. However, looking at the prompt "Please translate the following content", and the input has tags, I will output the text with the corresponding formatting (bold/italics) or just clean text? * *Decision on HTML:* The user provided HTML tags. A professional translation usually preserves the format. I will output the text with the formatting applied (bold/italics) but without the raw HTML tags visible, *unless* the user wants the HTML code back. The prompt says "output the translation result". Usually, this means rendered text. However, to be safe and precise regarding "technical details", I will render the text but maintain the structure (paragraphs). * *Wait, looking at the prompt again:* "只输出翻译结果" (Only output the translation result). If I output raw HTML, it might look like code. If I output plain text, it loses the bold/italic distinction. I will provide the translation in a clean, formatted text style that mirrors the input structure (using bolding and italics where the tags indicated). * *Refining the Funding Section